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Statistics By Jim

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Hypothesis Testing: Uses, Steps & Example

By Jim Frost 4 Comments

What is Hypothesis Testing?

Hypothesis testing in statistics uses sample data to infer the properties of a whole population . These tests determine whether a random sample provides sufficient evidence to conclude an effect or relationship exists in the population. Researchers use them to help separate genuine population-level effects from false effects that random chance can create in samples. These methods are also known as significance testing.

For example, researchers are testing a new medication to see if it lowers blood pressure. They compare a group taking the drug to a control group taking a placebo. If their hypothesis test results are statistically significant, the medication’s effect of lowering blood pressure likely exists in the broader population, not just the sample studied.

Using Hypothesis Tests

A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement the sample data best supports. These two statements are called the null hypothesis and the alternative hypothesis . The following are typical examples:

• Null Hypothesis : The effect does not exist in the population.
• Alternative Hypothesis : The effect does exist in the population.

Hypothesis testing accounts for the inherent uncertainty of using a sample to draw conclusions about a population, which reduces the chances of false discoveries. These procedures determine whether the sample data are sufficiently inconsistent with the null hypothesis that you can reject it. If you can reject the null, your data favor the alternative statement that an effect exists in the population.

Statistical significance in hypothesis testing indicates that an effect you see in sample data also likely exists in the population after accounting for random sampling error , variability, and sample size. Your results are statistically significant when the p-value is less than your significance level or, equivalently, when your confidence interval excludes the null hypothesis value.

Conversely, non-significant results indicate that despite an apparent sample effect, you can’t be sure it exists in the population. It could be chance variation in the sample and not a genuine effect.

Learn more about Failing to Reject the Null .

5 Steps of Significance Testing

Hypothesis testing involves five key steps, each critical to validating a research hypothesis using statistical methods:

• Formulate the Hypotheses : Write your research hypotheses as a null hypothesis (H 0 ) and an alternative hypothesis (H A ).
• Data Collection : Gather data specifically aimed at testing the hypothesis.
• Conduct A Test : Use a suitable statistical test to analyze your data.
• Make a Decision : Based on the statistical test results, decide whether to reject the null hypothesis or fail to reject it.
• Report the Results : Summarize and present the outcomes in your report’s results and discussion sections.

While the specifics of these steps can vary depending on the research context and the data type, the fundamental process of hypothesis testing remains consistent across different studies.

Let’s work through these steps in an example!

Hypothesis Testing Example

Researchers want to determine if a new educational program improves student performance on standardized tests. They randomly assign 30 students to a control group , which follows the standard curriculum, and another 30 students to a treatment group, which participates in the new educational program. After a semester, they compare the test scores of both groups.

Download the CSV data file to perform the hypothesis testing yourself: Hypothesis_Testing .

The researchers write their hypotheses. These statements apply to the population, so they use the mu (μ) symbol for the population mean parameter .

• Null Hypothesis (H 0 ) : The population means of the test scores for the two groups are equal (μ 1 = μ 2 ).
• Alternative Hypothesis (H A ) : The population means of the test scores for the two groups are unequal (μ 1 ≠ μ 2 ).

Choosing the correct hypothesis test depends on attributes such as data type and number of groups. Because they’re using continuous data and comparing two means, the researchers use a 2-sample t-test .

Here are the results.

The treatment group’s mean is 58.70, compared to the control group’s mean of 48.12. The mean difference is 10.67 points. Use the test’s p-value and significance level to determine whether this difference is likely a product of random fluctuation in the sample or a genuine population effect.

Because the p-value (0.000) is less than the standard significance level of 0.05, the results are statistically significant, and we can reject the null hypothesis. The sample data provides sufficient evidence to conclude that the new program’s effect exists in the population.

Limitations

Hypothesis testing improves your effectiveness in making data-driven decisions. However, it is not 100% accurate because random samples occasionally produce fluky results. Hypothesis tests have two types of errors, both relating to drawing incorrect conclusions.

• Type I error: The test rejects a true null hypothesis—a false positive.
• Type II error: The test fails to reject a false null hypothesis—a false negative.

Learn more about Type I and Type II Errors .

Our exploration of hypothesis testing using a practical example of an educational program reveals its powerful ability to guide decisions based on statistical evidence. Whether you’re a student, researcher, or professional, understanding and applying these procedures can open new doors to discovering insights and making informed decisions. Let this tool empower your analytical endeavors as you navigate through the vast seas of data.

Learn more about the Hypothesis Tests for Various Data Types .

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Reader Interactions

June 10, 2024 at 10:51 am

Thank you, Jim, for another helpful article; timely too since I have started reading your new book on hypothesis testing and, now that we are at the end of the school year, my district is asking me to perform a number of evaluations on instructional programs. This is where my question/concern comes in. You mention that hypothesis testing is all about testing samples. However, I use all the students in my district when I make these comparisons. Since I am using the entire “population” in my evaluations (I don’t select a sample of third grade students, for example, but I use all 700 third graders), am I somehow misusing the tests? Or can I rest assured that my district’s student population is only a sample of the universal population of students?

June 10, 2024 at 1:50 pm

I hope you are finding the book helpful!

Yes, the purpose of hypothesis testing is to infer the properties of a population while accounting for random sampling error.

In your case, it comes down to how you want to use the results. Who do you want the results to apply to?

If you’re summarizing the sample, looking for trends and patterns, or evaluating those students and don’t plan to apply those results to other students, you don’t need hypothesis testing because there is no sampling error. They are the population and you can just use descriptive statistics. In this case, you’d only need to focus on the practical significance of the effect sizes.

On the other hand, if you want to apply the results from this group to other students, you’ll need hypothesis testing. However, there is the complicating issue of what population your sample of students represent. I’m sure your district has its own unique characteristics, demographics, etc. Your district’s students probably don’t adequately represent a universal population. At the very least, you’d need to recognize any special attributes of your district and how they could bias the results when trying to apply them outside the district. Or they might apply to similar districts in your region.

However, I’d imagine your 3rd graders probably adequately represent future classes of 3rd graders in your district. You need to be alert to changing demographics. At least in the short run I’d imagine they’d be representative of future classes.

Think about how these results will be used. Do they just apply to the students you measured? Then you don’t need hypothesis tests. However, if the results are being used to infer things about other students outside of the sample, you’ll need hypothesis testing along with considering how well your students represent the other students and how they differ.

I hope that helps!

June 10, 2024 at 3:21 pm

Thank you so much, Jim, for the suggestions in terms of what I need to think about and consider! You are always so clear in your explanations!!!!

June 10, 2024 at 3:22 pm

You’re very welcome! Best of luck with your evaluations!

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Hypothesis Testing: Winning Jeopardy

Introduction.

Jeopardy is a popular TV show in the US where participants answer trivia to win money. Participants are given a set of categories to choose from and a set of questions that increase in difficulty. As the questions get more difficult, the participant can earn more money for answering correctly.

In June 2019, contestant James Holzhauer ended a 32-game winning streak, just barely missing the record for highest winnings. James Holzhauer dedicated hours of effort to optimizing what he did during a game to maximize how much money he earned. To achieve what he did, James had to learn and master the vast amount of trivia that Jeopardy can throw at the contestants.

Let’s say we want to compete on Jeopardy like James. As he did, we’ll have to familiarize ourselves with an enormous amount of trivia to be competitive. Given the vastness of the task, is there a way that we can somehow simplify our studies and prioritize topics that appear more often in Jeopardy? In this project, we’ll work with a dataset of Jeopardy questions to figure out some patterns in the questions that could help us win.

Data Import

Fixing data types.

The value column actually incorporates a dollar sign and uses the value None in places where the question came from a Final Jeopardy, the last question of every episode. The presence of these factors causes R to convert this column to a character instead of a numerical one. For our later analysis, we’ll need the value column to be numeric, so we should do this now.

Normalizing Text

One messy aspect about the Jeopardy dataset is that it contains text. Text can contain punctuation and different capitalization, which will make it hard for us to compare the text of an answer to the text of a question. We would like to make this process easier for ourselves, so we’ll need to process the text data in this step. The process of cleaning text in data analysis is sometimes called normalization. More specifically, we want ensure that we lowercase all of the words and any remove punctuation. We remove punctuation because it ensures that the text stays as purely letters. Before normalization, the terms Don’t and don’t are considered to be different words, and we don’t want this. For this step, normalize the question, answer, and category columns.

Making Dates More Accessible

In our last data cleaning step, we need to address the air_date column. Like value ’s original type, air_date is a character . Ideally we would want to separate this column into a year , month and day column to make filtering easier in the future. Furthermore, we would also want each of these new date columns to be numeric to make comparison easier as well.

Focusing On Particular Subject Areas

We are now in a place where we can properly ask questions from the data and perform meaningful hypothesis tests on it. Given the near infinite amount of questions that can be asked in Jeopardy, you wonder if any particular subject area has increased relevance in the dataset. Many people seem to think that science and history facts are the most common categories to appear in Jeopardy episodes. Others feel that Shakespeare questions gets an awful lot of attention from Jeopardy.

With the chi-squared test, we can actually test these hypotheses! For this exercise, let’s assess if science, history and Shakespeare have a higher prevalence in the data set. First, we need to develop our null hypotheses. There are around 3369 unique categories in the Jeopardy data set after doing all of our cleaning. If we suppose that no category stood out, we would expect that the probability of picking a random category would be the same no matter what category you picked. This comes out to be \(1/3369\) . This would also mean that the probability of not picking a particular category would be \(3368/3369\) . When we first learned the chisq.test() function when testing for the number of males and females in the Census data, we assumed that their proportion would be equal — that there would be a 50-50 split between them. The chisq.test() automatically assumes this of the data you provide it, but we can also specify what these proportions should be using the p argument.

We see p-values less than 0.05 for each of the hypothesis tests. From this, we would conclude that we should reject the null hypothesis that science doesn’t have a higher prevalence than other topics in the Jeopardy data. We would conclude the same with history and Shakespeare.

Unique Terms in Questions

Let’s say we want to investigate how often new questions are repeats of older ones. To start on this process, we can do the following:

• Sort jeopardy in order of ascending air date.
• Initialize an empty vector to store all the unique terms that are in the Jeopardy questions.
• For each row, split the value for question into distinct words, remove any word shorter than 6 characters, and check if each word occurs in terms_used.

Terms In Low and High Value Questions

Let’s say we only want to study terms that have high values associated with it rather than low values. This optimization will help us earn more money when we’re on Jeopardy while reducing the number of questions we have to study. To do this, we need to count how many high value and low value questions are associated with each term. We’ll define low and high values as follows:

• Low value: Any row where value is less than 800.
• High value: Any row where value is greater or equal than 800.

For each category, we can see that under this definition that for every 2 high value questions, there are 3 low value questions. Once we count the number of low and high value questions that appear for each term, we can use this information to our advantage. If the number of high and low value questions is appreciably different from the 2:3 ratio, we would have reason to believe that a term would be more prevalent in either the low or high value questions. We can use the chi-squared test to test the null hypothesis that each term is not distributed more to either high or low value questions.

To do this, we need:

• Create an empty dataset that we can add more rows to
• Iterate through all the different terms in terms_used.
• For each term:
• Iterate through all of the questions in the dataset and see if the term is present in each question.
• If the term is present in the question, we then need to check if the question is high or low value
• After iterating through all the questions, test the null hypothesis using the information we discussed above.
• Each term should be associated with a high value question count, a low value question count, and a p-value. Turn these values into a vector and append it to the empty dataset you created.

We can see from the output that some of the values are less than 5. Recall that the chi-squared test is prone to errors when the counts in each of the cells are less than 5. We may need to discard these terms and only look at terms where both counts are greater than 5.

From the 20 terms that we looked at, it seems that the term “indian” is more associated with high value questions. Interesting!

Here are some potential next steps:

• Manually create a list of words to remove, like the, than, etc.
• Find a list of stopwords to remove and use this instead.
• Remove words that occur in more than a certain percentage (like 5%) of questions.
• Another way of analyzing the “value” of each term might be to take all the values associated with it and calculate the “average value” of a term. This would give you a more quantitative idea of what terms are more high value than others.
• Use the whole Jeopardy dataset (available here instead of the subset we used in this lesson. Note that we’ll need to vectorize your code to make sure that our solution doesn’t run excessively long. The solution code uses for loops, which are slow for large amounts of data.
• Use phrases instead of single words when seeing if there’s overlap between questions. Single words don’t capture the whole context of the question well.

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Hypothesis Testing in Python

In this course, you’ll learn advanced statistical concepts like significance testing and multi-category chi-square testing, which will help you perform more powerful and robust data analysis.

Part of the Data Analyst (Python) , and Data Scientist (Python) paths.

• Intermediate friendly

“Dataquest teaches you how you do data analysis in the real world. Dataquest is well-suited for folks with busier schedules. The lessons are broken into smaller chunks, so it’s really conducive to that. You only have an hour, okay, well, just do one or two lessons and that’s fine.”

Stacey Ustian

Course overview.

In this course, you’ll learn about single and multi-category chi-square tests, degrees of freedom, hypothesis testing, and different statistical distributions.

To learn about hypothesis testing and statistical significance, you’ll work hands-on with multiple datasets on weight loss data — are patients losing weight due to pure luck, or is it a diet pill? You’ll run the numbers and find out!

At the end of the course, you’ll complete a guided project in which you’ll work with data from the American TV show Jeopardy. You’ll analyze text and search for winning strategies. It’s a chance for you to combine the skills you learned in this course, and to showcase a fascinating project in your portfolio. Best of all, you’ll learn by doing — you’ll practice and get feedback directly in the browser.

• Defining regular and multi-category chi-squared tests
• Performing significance testing to understand an outcome's importance

Course outline

Hypothesis testing in python [4 lessons], significance testing 1h.

• Explain how hypothesis testing works
• Define the relation between statistical significance and hypothesis testing

Chi-Squared Tests 1h

• Determine the statistical significance of a set of categorical values
• Generate the chi-squared distribution
• Define degrees of freedom

Multi-Category Chi-Squared Tests 1h

• Extend chi-squared tests to multiple categories
• Calculate the statistical significance of multi-category chi-squared tests

Guided Project: Winning Jeopardy 1h

• Answer questions using text data
• Apply chi-squared tests to real problems

Projects in this course

Guided project: winning jeopardy.

For this project, you’ll take on the role of a Jeopardy contestant looking for any edge to win. You’ll work with a dataset of 20,000 Jeopardy questions using Python and pandas to analyze question and answer text and uncover helpful patterns.

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Employed teachings from Codecademy Data Science pathway to analyze .csv file containing 216,931 jeopardy questions. Focused on cleaning and analyzing this large dataset. Concluded with developing a random question generator.

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Health-Related Quality of Life in Older Adults: Testing the Double Jeopardy Hypothesis (Journal of Aging Studies)

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• Andrew Noymer

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Double Jeopardy? Age, Race, and HRQOL in Older Adults with Cancer

Keith m. bellizzi.

1 Department of Human Development and Family Studies, University of Connecticut Storrs, CT 06269, USA

Noreen M. Aziz

2 Division of Cancer Control Population Sciences, National Cancer Institute, Rockville, MD 20852, USA

Julia H. Rowland

Kathryn weaver.

3 Department of Social Sciences Health Policy, Wake Forest University School of Medicine, Winston-Salem, NC 27104-4225, USA

Neeraj K. Arora

Ann s. hamilton.

4 Keck School of Medicine of USC, University of Southern California, Los Angeles, CA 90089, USA

Ingrid Oakley-Girvan

5 Cancer Prevention Institute of California, Fremont, CA 94538, USA

Gretchen Keel

6 Information Management Services, Silver Spring, MD 20904, USA

Understanding the post-treatment physical and mental function of older adults from ethnic/racial minority backgrounds with cancer is a critical step to determine the services required to serve this growing population. The double jeopardy hypothesis suggests being a minority and old could have compounding effects on health. This population-based study examined the physical and mental function of older adults by age (mean age = 75.7, SD = 6.1), ethnicity/race, and cancer (breast, prostate, colorectal, and gynecologic) as well as interaction effects between age, ethnicity/race and HRQOL. There was evidence of a significant age by ethnicity/race interaction in physical function for breast, prostate and all sites combined, but the interaction became non-significant (for breast and all sites combined) when comorbidity was entered into the model. The interaction persisted in the prostate cancer group after controlling for comorbidity, such that African Americans and Asian Americans in the 75–79 age group report lower physical health than non-Hispanic Whites and Hispanic Whites in this age group. The presence of double jeopardy in the breast and all sites combined group can be explained by a differential comorbid burden among the older (75–79) minority group, but the interaction found in prostate cancer survivors does not reflect this differential comorbid burden.

1. Introduction

By 2030, nearly one in five US residents will be >65 years of age and this group is projected to reach 72 million by that year, a doubling of the number in 2008 [ 1 ]. During this period, it is estimated that the percentage of all cancers diagnosed in older adults and ethnic/racial minorities will increase from 61% to 70% and from 21% to 28%, respectively [ 2 ]. Historically, older adults and minorities have been underrepresented in cancer clinical trials which can ultimately lead to disparities in treatment and outcomes. An important outcome that has received little attention is the posttreatment health-related quality of life (HRQOL) of older adults with cancer from minority backgrounds. The double jeopardy hypothesis suggests that being a minority and old could have additive negative effects on health outcomes [ 3 – 5 ]. Understanding the post-treatment burden of older adults and minorities with cancer is a critical step to determine the services and resources required to serve this rapidly growing population.

While the long-term surveillance of older adults and minorities with cancer is limited, evidence suggests physical and social functioning are the most common HRQOL domains affected by cancer and its treatment, with mixed findings for mental health for this group of survivors [ 6 – 12 ]. A population-based study of 703 adult breast cancer survivors found significant ethnic differences in HRQOL, with Latinos reporting greater role limitations and lower emotional well-being than Caucasians, African Americans, and Asian Americans [ 11 ]. Another study, focused on disparities in older cancer survivors and non-cancer-managed care enrollees, found physical and mental function were lower in Hispanic cancer survivors compared with Caucasian and African Americans [ 8 ]. Deimling and colleagues found older, African American cancer survivors experience poorer functional health and higher levels of comorbidity and decreased physical functioning after cancer compared with older Caucasian cancer survivors [ 7 ]. Most recently, a prospective study of 1,432 older cancer survivors and 7,160 matched controls found significant declines in physical function and mental health across several cancer sites relative to the mean change of the control group [ 13 ]. Despite the contribution of these few studies to our understanding of HRQOL in older adults from minority backgrounds, they are mostly confined to survivors of prostate or breast cancer or are restricted to short-term (i.e., less than 5 years) survivors. Importantly, studies that have examined the effect of age and race have done so in isolation without attention to possible interaction effects between these important, yet understudied correlates of HRQOL. Other factors found to be related to quality of life in cancer survivors, including optimism, perceived control, and social support were also examined to control for these effects on HRQOL outcomes [ 9 , 11 ].

To examine the relationship between age and race/ethnicity with HRQOL among cancer survivors, we conducted one of the largest population-based studies of long-term, ethnically diverse, adult cancer survivors in the United States. The overall goal of the study was to obtain information regarding medical follow-up care and late health effects, including HRQOL during the extended survivorship years to facilitate the development of standards or best practices for such care. The specific objectives of these analyses were: (1) to examine the HRQOL of older long-term cancer survivors by cancer type (breast, prostate, colorectal, and gynecologic cancer), ethnicity/race (non-Hispanic White, Hispanic White, African American and Asian American) and age group (65–74, 75–84 and 85 plus) and (2) to examine potential interaction effects between age and ethnicity/race as well as other demographic, health, and psychosocial correlates of HRQOL in older long-term cancer survivors. We hypothesized that there would be a significant interaction effect between minority status and age, with ethnic/racial minority disparities in HRQOL increasing with age.

2.1. Participants and Procedures

Study subjects were men and women who participated in the Follow-Up Care Use of Cancer Survivors (FOCUS) Study, a population-based, cross-sectional study of ethnically diverse adult survivors of breast, prostate, colorectal, ovarian, and endometrial cancers from northern and southern California funded by the National Cancer Institute. Selected patients were mailed a detailed questionnaire to complete on their own and return in a postage paid envelope. Extensive telephone followup was conducted and additional questionnaire mailings were sent in efforts to reach patients and increase response rates. The study was approved by the institutional review boards at the Cancer Prevention Institute of California (CPIC, formerly known as the Northern California Cancer Center (NCCC)) and the University of Southern California (USC), Los Angeles, in accord with an assurance filed and approved by the US Department of Health and Human Services.

The cancer patients were selected from the CPIC and the Los Angeles County Cancer Surveillance Program, cancer registries that are members of the Surveillance, Epidemiology, and End Results (SEER) program. To be eligible, patients had to be English speaking, adults at least 21 years of age at diagnosis, have a primary diagnosis of breast, prostate, colorectal, ovarian, or endometrial cancer and have completed treatment. Case selection was stratified by cancer site, time since diagnosis, age group, and race/ethnicity to provide sufficient sample size in each subgroup for analyses. Specifically, time since diagnosis was dichotomized between an average of 6 (4 to 8) and 12 (10–15) years after initial cancer diagnosis. Age group included those <65 and 65+, while race/ethnicity was stratified by ethnicity/race: non-Hispanic White, African American, Hispanic White, and Asian American.

Of the 6,391 selected cases (not known to be deceased at the time of sample selection), 4,981 (78%) were eligible after we eliminated those who were found to be deceased after attempts to contact ( n = 415), unable to understand English ( n = 477), too ill to participate ( n = 289), said they never had cancer ( n = 142), whose physician did not provide consent ( n = 42), or were otherwise ineligible ( n = 45; e.g., in active treatment, out of the country). Of the 4,981 eligible, an additional 2,004 (40%) could not be located after multiple efforts were made to trace and locate them, (using web-based tracing services such as “reach411”, “Intelius,” “Masterfiles,” and “Acxiom”,) yielding a total of 2,977 eligible cases who were reached. Of these, 1,666 (56%) completed the mailed survey for the FOCUS study. Upon review of the surveys, a further 84 cases where the respondent indicated he/she was not in treatment were removed from all analyses leaving a final sample of 1,582 cases.

Multivariable logistic regression was used to determine factors related to participant response. Among the 4,981 eligible selected cases, those 65 and older, those with colorectal cancer, and those diagnosed longer ago were less likely to participate. Lastly, as this paper focused on outcomes for older adults (≥65 years of age), those in the sample younger than 65 ( N = 511; 32%) were excluded resulting in an analytic sample that included 1,071 study respondents.

Eligible study participants were mailed a self-report study questionnaire containing a number of standardized measures to assess psychosocial and HRQOL variables along with questions assessing late health effects and follow-up care patterns specific to the larger FOCUS project. Included in the mailing was an introductory letter describing the purpose of the study and a prepaid return envelope. If the survey had not been returned after three weeks, the survivors were called to make sure they had received the questionnaire, answer any questions, and encourage them to send in the questionnaire. Upon return of the completed questionnaire, study participants received either a $20 (LA County Cancer Surveillance Program) or $25 (CPIC) check and a thank you letter.

2.2. Measures

2.2.1. demographic and disease characteristics.

Self-reported socio-demographic information included age, sex, ethnicity/race, marital status, education, and health insurance. While household income was collected, the percent (11%) of missing data from this variable was significantly higher than the percent missing for education (1.4%); thus the decision was made to use education as a proxy for SES as opposed to both education and income. Additionally, income and education were highly correlated in this sample. Health-related characteristics, including type of treatment, cancer history, and disease stage were collected via SEER registry data. Based on SEER historic staging information, stage of disease was characterized as local, regional, and distant for breast, colorectal and gynecologic, whereas prostate cancer stage was differentiated as local and regional or distant. Times since diagnosis and comorbid medical conditions (checklist of 39 medical conditions, including irregular heartbeat, heart failure, cardiomyopathy, heart attack, angina, hypertension, pericarditis, leaking heart valves, blood clots, stroke, epilepsy, seizures, neuropathy, chronic lung disease, asthma, pleurisy, lung fibrosis, pneumonia, abnormal liver function, liver disease, inflammatory bowel disease, gallbladder problems, kidney stones, kidney or bladder infections, hyperthyroid, hypothyroid, diabetes, osteoporosis, avascular necrosis, partial or complete deafness, cataracts, problems with retina, arthritis, lymphedema, anemia, shingles, sciatica, and fertility issues) were collected via self-report. The comorbidity checklist was adapted from previous studies on cancer [ 14 , 15 ].

2.2.2. Health-Related Quality of Life

Two summary scores from the Short Form–12 were used to measure HRQOL [ 16 , 17 ]. These included the physical component summary (PCS) score and mental component summary (MCS) score constructed on the basis of the 1999 US population norms with a mean value of 50 that represented the US population norms and a standard deviation of 10.

2.2.3. Psychosocial Factors

The Life Orientation Test-Revised (LOT-R) was used to measure optimism [ 18 ]. The LOT-R is a 6-item scale including items such as “In uncertain times, I usually expect the best.” The scale has exhibited good reliability and validity in use with chronically ill populations, including cancer patients [ 9 , 19 ]. Cronbach's alpha for the six items in the current study was .93. The 12-item short form of the MOS Social Support scale was used to assess social support [ 20 , 21 ]. For each item, the respondent was asked to indicate how often social support was available to him or her if needed. Response options ranged from “none of the time” to “all of the time.” Items were summed and transformed into a scale of 0 to 100. Cronbach's alpha for the Social Support scale in the current study was .95. Perceived control was measured using a 4-item scale used in an earlier study. [ 14 ] Respondents were asked to indicate the extent of control they have over aspects of cancer, including “emotional responses to your cancer”, “physical side effects of your cancer and its treatment”, “the course of your cancer (i.e., whether cancer will come back or get worse)”, and “the kind of follow-up care you receive for your cancer.” Response options ranged from “no control at all” to “complete control”. The four items were summed and transformed into a scale of 0 to 100. Cronbach's alpha for these four items was .88.

2.3. Analytic Plan

Descriptive statistics were used to describe the demographic, health, and psychosocial characteristics of the sample. Separate general linear models (GLMS) were run for all cancer sites combined as well as for each specific cancer site to test the main effects of independent variables (age, ethnicity/race, education, medical comorbidities, optimism, and social support) and the interaction effects of age and ethnicity/race on physical and mental health. Variables included in these multivariable models were significantly associated ( P < .05) with HRQOL at the bivariate level using χ 2 tests for categorical variables and t tests for continuous variables. The following variables not associated with HRQOL in bivariate analyses were not included in the final model: gender, cancer stage, health insurance coverage, time since diagnosis, SEER site and type of cancer treatment received, and perceived control. Blocks of variables were entered into the models sequentially to examine the impact of each category of factors (demographic, health, and psychosocial) on HRQOL. Adjusted means and standard errors of outcome measures by categorical demographic and health characteristics were calculated using general linear modeling (GLM) and beta coefficients and standard errors of outcomes were generated for continuous variables. Tukey's post hoc tests were used to detect significant differences. Estimated marginal means were used to plot the effects of age and race on HRQOL. Analyses were conducted using SPSS version 16.

3.1. Sample Characteristics

The analytic sample consisted of 1,071 men and women aged 65 years or older (Mean = 75.7, SD = 6.1) diagnosed with confirmed cases of breast, prostate, colorectal, or gynecologic cancer. The gynecologic cancer group included both endometrial and ovarian cancers due to insufficient sample sizes to permit separate analyses for each group. Table 1 displays other characteristics of the sample. Average time since diagnosis was 9 years (SD = 3.2). Two-thirds of the sample was represented by ethnic/racial minority groups providing sufficient sample size for testing age/race interaction effects on HRQOL. The sample consisted of slightly more ( P < .05) females (61%) than males. Table 2 shows the mean scores and standard deviation for the psychosocial and HRQOL scales. Physical and mental HRQOL scores across all cancer sites were marginally lower than general US population norms for individuals aged 65 years or older [ 16 ].

Sample characteristics (%).

∗ The high rate of distant disease in the gynecologic group reflects higher rates of distant disease in African American women with endometrial cancer, which is comparable to rates in the US population.

Unadjusted mean scores and standard deviations for psychosocial/HRQOL scales.

∗ Scored on a 0–24 scale (higher scores reflect higher optimism).

† Scored on a 0–100 scale (higher scores reflect more social support).

‡ Constructed on the basis of the 1999 US population norms with a mean value of 50 that represented the US population norms and a standard deviation of 10. Higher scores reflect better function.

3.2. Correlates of HRQOL in Ethnically Diverse Older Adults with Cancer

Using the GLM procedure, adjusted mean scores were calculated to examine the association between demographic, health related, and psychosocial factors with physical and mental health ( Table 3 ). The following section describes the results of the GLM procedure overall (all sites combined) and across the different cancer sites.

Adjusted mean HRQOL scores † by demographic, health, and psychosocial characteristics.

† Adjusted for all other variables in the model.

‡ NHW: non-Hispanic White; HW: Hispanic White; AA: African American.

Note: values in bold indicate P value <.05 from overall F -test.

Different letters denote statistically significant differences using Tukey's post hoc tests.

3.3. Physical HRQOL

The combined variables in the overall model accounted for 29% (adjusted R 2 ) of the variance in physical HRQOL with demographics accounting for 6%, comorbidity accounting for 19%, and psychosocial factors accounting for 5%. In the overall model, as well as the breast and prostate cancer group, the interaction effect between age and race was significant when entered into the models with the demographic factors, but the effect became nonsignificant in the overall model and breast cancer model once comorbidity was entered into the models. In the overall model, the pattern of interaction was such that African Americans in the 75–79 age group reported lower physical health than non-Hispanic Whites and Hispanic Whites in this age group (see Figure 1 ). This same pattern existed in the breast cancer group, but these data also showed that Hispanic Whites in the 75–79 age group reported higher physical health scores compared to African American and Asian Americans in this age group. The comorbid burden among all cancer sites combined, as well as the breast cancer group, is significantly ( P < .05) greater than the comorbid burden in the prostate cancer group ( Table 1 ). To explore this pattern further, analysis of variance was conducted to see if there was a differential comorbid pattern in African Americans in the 75–79 age group compared to other ethnic/racial groups in this age range. Results indicated that African American breast cancer survivors in this age group reported, on average, 9.6 comorbid conditions (SD = 5.5) compared with 5.3 for non-Hispanic Whites (SD = 3.7), 6.3 for Hispanic Whites (SD = 2.4), and 5.8 for Asian Americans (SD = 3.4) (all P's < .05). This pattern was similar in the overall model.

Age by race/ethnicity interaction plots (PCS).

With respect to prostate cancer, the significant interaction persisted after entering comorbidity and other psychosocial variables into the model ( β = 9.16, SE = 4.5, P < .01). African Americans and Asian Americans in the 75-79 age group reported lower PCS scores than non-Hispanic Whites and Hispanic Whites. These scores were greater in the oldest age group, (80 plus) for African Americans and Asian Americans with a significant difference between African Americans' scores and non-Hispanic Whites' scores on physical HRQOL ( Figure 1 ).

Other findings of interest (see Table 3 ) include older age significantly associated with lower PCS scores, overall ( P < .01) and in the breast and colorectal groups (all Ps < .05). PCS scores for African Americans and Asian Americans in the breast, prostate and “all sites combined” models were significantly lower than non-Hispanic Whites and Hispanic Whites ( P < .01). Across all cancer sites, education was significantly associated (Cohen's d effect size = .3) with PCS in that those with a college degree and/or graduate degree had higher PCS scores than all those groups with lower educational attainment (all Ps < .05). A more pronounced relationship between low education and PCS was found in the breast and prostate groups where those survivors without a high school diploma or GED reported PCS scores nine points lower than the survivors with the same education in the colorectal and gynecologic groups. More comorbid conditions were significantly associated with worse PCS ( P < .01), overall and across the four cancer sites. Social support was not related to PCS, but higher optimism was significantly associated with better PCS ( P < .01) overall and across three of the four sites (i.e., breast cancer, nonsignificant).

3.4. Mental HRQOL

Investigation of MCS scores showed that the variance explained by the set of independent variables in the overall model was 22% (adjusted R 2 ). Unlike PCS scores, the psychosocial variables explained the majority of the variance in mental HRQOL with optimism = 11% and social support = 4%. The remaining variance was explained by demographics (4%) and health factors (3%). In contrast to PCS results, the age-race/ethnicity interaction effect was not significant in the overall model or site-specific models regardless of when it was entered into the model. Overall and in the breast cancer group older age was associated with higher MCS score (all Ps < .05). Additionally, having a college degree or having some college experience was significantly associated with higher scores on MCS compared with graduating from high school or obtaining a GED ( Ps < .01) in the colorectal group and in all sites combined. Those with more comorbid conditions reported worse MCS ( P < .01), overall and across the four cancer sites. The overall model as well as the site-specific models show higher scores on social support and optimism was significantly associated with higher scores on MCS ( Ps < .05).

4. Discussion

This population-based study examined the HRQOL of older long-term cancer survivors by cancer type, ethnicity/race and age as well as potential interaction effects between age, ethnicity/race, and HRQOL. We found that the double jeopardy effect of being an ethnicity/racial minority and older persisted for the overall sample (all sites combined) and the breast cancer group when entered into the model with demographic variables, but the effect went away after controlling for comorbidity. Double jeopardy persisted in the prostate cancer group even after controlling for comorbidity. Different predictors accounted for differing amounts of variance in PCS and MCS scores. In general psychosocial factors were more strongly associated with MCS, while medical comorbidities were more strongly associated with PCS.

The presence of double jeopardy in the overall model (likely driven by the breast cancer group) as well as the breast cancer model could potentially be explained by the higher comorbid burden among African American cancer patients in the middle age group compared to this group in the other cancer sites. The importance of monitoring for comorbidities, especially in older minority breast cancer survivor populations, and ensuring adequate control of these conditions should be of particular concern and is becoming a growing focus of attention in the oncology community [ 22 , 23 ].

There was evidence to support the existence of double jeopardy in our sample of prostate cancer survivors even after controlling for comorbid conditions. Future research should further explore this interaction as prostate cancer is the most prevalent cancer in older men and African American men are at greater risk compared to white men. Additionally, African American men generally have more advanced disease when diagnosed [ 24 ]—perhaps due to delay in diagnosis because of poorer screening rates and access to care. However, stage of disease was not significantly related to HRQOL thus likely did not account for the presence of double jeopardy in this group. It is important to note that our prostate cancer group was quite homogeneous with respect to stage (95% local/regional), so there was little variability to adequately test the association of stage of disease on HRQOL in that group. Figure 1 suggests a higher score in physical function in the oldest age group for African American and Asian Americans compared to non-Hispanic Whites perhaps suggesting a resiliency effect. It is conceivable that the oldest age group reflects a more adaptive and healthy cohort or the younger race-specific cohorts were exposed to events or treatments with long-term impacts on physical function. A healthy survivor bias may also explain this effect. Although there is a 6.2-year reduction in life expectancy at birth for African American males compared to White males, this narrows to 2.2 years at age 65 and only .7 years at age 75 (CDC, Health, United States, 2008). This suggests, that for those African American men who survive to age 75, black-white differences in health may not be as pronounced.

A few additional findings warrant special note. Consistent with other studies [ 8 , 12 ], these data suggest that race/ethnicity influences physical functioning above and beyond socioeconomic status. African American and Asian American cancer survivors (all sites combined) reported significantly lower PCS scores compared with White and Hispanics, even after controlling for education. This effect also persisted after controlling for noncancer medical comorbidities. These data suggest that clinicians should potentially anticipate differences in older adults from some minority backgrounds, as they may be at risk for greater decrements in physical function as a result of their cancer and treatment. Level of education was found to positively influence not only survivors' reports of physical health (PCS) but also mental health (MCS). A buffering effect of education on illness outcomes has been shown by others [ 7 , 8 , 12 ] and may be a function of the association between more education and increased coping skills, better access to optimal healthcare, including preventive services (contributing to a stronger feeling of control over health care) and greater investment in positive health behaviors. To the extent that racial disparities continue to persist in access to education, this has implications for the future health of these populations.

Not surprisingly, the presence of competing comorbid conditions was found to adversely affect both mental and physical health outcomes. On average, the survivors in this study reported more than five non-cancer comorbidities. In some cases, with cancer survivors now living longer, co-morbid condition may include the diagnosis of a second or third malignancy [ 25 ]. Careful assessment of comorbid conditions prior to cancer treatment and across the cancer survivorship trajectory is warranted in all populations of survivors.

Strengths of this study are its population-based stratified sampling method, inclusion of large numbers of older survivors, attention to long-term (5–14 years after diagnosis) survivors' function, and well-being, examination of the four cancer sites for which we have the most prevalent populations of survivors, as well as recruitment of sufficient numbers of minority groups to enable examination of race/ethnicity by age interaction effects on survivors' HRQOL outcomes. However, there are a number of limitations to these data. As noted earlier, those who were sicker, whether due to cancer or other comorbid conditions, non-English speaking, longer-term survivors, and those who were hard to reach (potentially because they had moved to locations where care is delivered by extended family or in assisted living or nursing home facility), did not participate in this survey. Thus, it is not clear how generalizable the present findings are to the broader population of older cancer survivors. This differential pattern of response (or dropout) could account for the unexpected observation that older (80 plus) prostate cancer survivors of Asian and African American background reported better physical HRQOL than their younger (75–79) counterparts. Although this is a cross-sectional study, it was nonetheless interesting to note that, while PCS scores for prostate cancer survivors were similar across ethnic/racial groups in the 65–74 age category, there was considerable divergence on this variable among those in the oldest age category. A further limitation to this study is that, while likely to be a rare occurrence, there is no way of knowing whether a caregiver or family member may have completed the surveys on the survivor's behalf.

Understanding the impact of cancer on HRQOL of older adults from minority backgrounds is of great importance. With the aging of Americans and demographic changes in the ethnic/racial composition of the US population, clinicians need to better anticipate, predict, and treat the physical and mental consequences of cancer and its treatment in specific segments of the population. The current study provides information regarding the physical and mental functioning of older adults from minority backgrounds as well as correlates that can be used to target clinical assessments and interventions. Our study suggests double jeopardy exists in the overall sample and breast cancer survivors, but is explained by differential burden of comorbid conditions in the middle age group for African Americans. Examining the reasons why double jeopardy persists in men with prostate cancer, after controlling for comorbidity warrants further attention. To what extent the compounding effect of age and race on physical function in the middle age group are the result of poorer access to care or delays in screening, and diagnosis in this group is not known, but worthy of future study.

The three types of T-Tests

What is Single-Sample, Independent-Samples, and Repeated Measures?

When to use a Z-Test

What is when comparing a sample with a population in which you know the mean and standard deviation?

Difference between One-Way ANOVA and Repeated-Measures ANOVA

What is Repeated-Measures ANOVA has a second parsing?

Definition of Correlation

What is a hypothesis test that is used in a research design in which there is one sample measured on two continuous variables (X & Y)?

The level Hypothesis Testing Occurs

What is Sample level?

How to compute the critical level

What is Degrees of Freedom (df)?

The value for Z in a Z-test

What is plus or minus 1.96

How to measure effect size in an ANOVA

What is eta-squared?

1.) r can range from -1.00 to +100

2.) r cannot exceed +/- 1.00

3.) two pieces of information are communicated (strength of relationship and # value)

The rare event range

What is alpha level equals either 0.05 or 0.01?

How to compute effect size

What is Cohen's d?

Reject the null hypothesis

What is value for Z-test must meet or exceed either Z=-1.96 or Z=+1.96

Why an ANOVA is different than a Z or T test

What is comparing more than two means?

The rules determining strength of relationship

What is the more closely the points cluster, the stronger the relationship or the more spread apart the points the weaker the relationship?

The difference between Type 1 and Type 2 error

What is Type 1 error equals a false positive and Type 2 error equals a false negative?

Criteria to determine effect size

What is 

Small: d is about 0.20

Mod: d is about 0.50

Large: d is about 0.80

The denominator of the Z-test Test Statistic

What is compute the value for sampling error/standard error?

The two sources of variability

What is Between groups variance and within groups variance?

Determining direction of relationship based on +/-

What is when r is positive there is a direct relationship between X & Y and when r is negative X & Y are inversely related?

The primary purpose of computing Effect Size

What is to determine whether the inferential decision (to reject the null or fail to reject the null hypothesis) was the correct or incorrect decision?

How to determine when to use each T-Test

1.) Single-Sample: one sample compared to a population

2.) Independent-Sample: two samples compared to each other

3.) Repeated-Measures: one sample, measured twice, compare time 1 to time 2

Inferential decision and effect size disagree

What is making either a type 1 or type 2 error?

What is compute Tukey's HSD and determine statistically different pairs?

The three computations for test statistic

1.) compute sum of products (SP)

2.) compute SS x and SS y

3.) compute r

The 5 steps of the Hypothesis Testing Procedure

1.) State hypothesis and set alpha level

2.) Find the CL that defines the CR

3.) Collect data and compute test statistic

4.) Make an inferential decision and interpret

5.) Compute effect size and interpret results

Hypothesis Testing

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