PSYC FPX 4700 Assessment 3 Hypothesis Effect Size Power and Tests

Grace J.
October 4, 2026October 4, 2026
BS Psychology, PSYC-FPX4700

Student Name

Capella University

PSYC FPX 4700 Statistics for the Behavioral Sciences

Prof. Name

Date

Hypothesis, Effect Size, Power, and t Tests

Hypothesis testing, effect size, statistical power, and t tests are fundamental concepts in psychological and behavioral research. They help researchers determine whether observed differences are statistically meaningful, estimate the magnitude of an effect, and evaluate whether a sample provides enough evidence to draw conclusions about a population. In this assessment, you will apply these concepts to sampling distributions, hypothesis testing, effect size and power, confidence intervals, and one-sample and independent-samples t tests using JASP and Excel.

Complete all problems in the designated Word document. Do not submit additional files. For problems that require mathematical calculations, show your work clearly. Make sure each final answer is easy to identify; you may use bold text, highlighting, or a different font color to distinguish answers from your calculations.

Problem Set 3.1: Sampling Distribution of the Mean

Criterion: Interpret population mean and variance.

A sampling distribution provides information about how sample statistics are distributed across repeated samples. Understanding the population mean and variance is important because these values provide the foundation for interpreting sample results.

Suppose a researcher wants to investigate the mean attention span of individuals in a hypothetical population. Attention span is measured as the amount of time, in minutes, that an individual remains focused on a particular task. The population is normally distributed, with the parameters provided in the original problem.

Use the information provided in the problem to answer the following questions:

1. What is the population mean (μ)?

Answer: __________________________

2. What is the population variance (σ²)?

Answer: __________________________

3. Sketch the population distribution.

Draw a normal distribution curve and clearly label the population mean and the values representing plus and minus three standard deviations from the mean. Your diagram should show:

μ − 3σ
μ − 2σ
μ − 1σ
μ
μ + 1σ
μ + 2σ
μ + 3σ

A correctly labeled normal distribution should be symmetrical around the population mean.

Problem Set 3.2: Effect Size and Statistical Power

Criterion: Explain effect size and power.

Effect size describes the magnitude of a difference or relationship, while statistical power refers to the probability that a statistical test will detect an effect when a true effect exists. In general, larger effect sizes and larger sample sizes increase statistical power. Smaller variability can also increase the ability to detect an effect.

Read each scenario and determine which researcher has greater statistical power, assuming all other factors remain equal.

Scenario 1: Effect Size

Two researchers conduct studies examining the effectiveness of a drug-use treatment. Researcher A finds an effect size of d = 0.36 among males, whereas Researcher B finds an effect size of d = 0.20 among females.

Which researcher has greater power to detect an effect? Explain your answer.

Answer: __________________________

The researcher with the larger effect size is expected to have greater statistical power when all other factors are equal because larger effects are generally easier for a statistical test to detect.

Scenario 2: Sample Size

Two researchers investigate marital satisfaction among military families. Researcher A studies 22 married couples (n = 22), while Researcher B studies 40 married couples (n = 40).

Which researcher has greater power to detect an effect? Explain your answer.

Answer: __________________________

When other factors are equal, the researcher using the larger sample is expected to have greater statistical power because larger samples generally provide more precise estimates and reduce sampling variability.

Scenario 3: Population Standard Deviation

Two researchers examine standardized examination performance among senior high school students in two local communities. Researcher A studies students from a northern community where the population standard deviation is σ = 110. Researcher B studies students from a southern community where the population standard deviation is σ = 60.

Which researcher has greater power to detect an effect? Explain your answer.

Answer: __________________________

When all other factors are equal, the researcher working with the smaller standard deviation is generally expected to have greater power because lower variability makes differences easier to detect.

Problem Set 3.3: Directional and Nondirectional Hypothesis Testing

Criterion: Explain the relationship between hypotheses, statistical tests, and the population mean.

Hypothesis testing allows researchers to compare competing explanations about a population. A directional hypothesis predicts the direction of a difference, while a nondirectional hypothesis predicts that a difference exists without specifying which group will have the higher value.

Cho and Abe (2013) discussed the appropriate use of one-tailed and two-tailed tests in behavioral research. Consider the following hypotheses for a study examining whether males self-disclose more than females:

H₀: μmales − μfemales ≤ 0

H₁: μmales − μfemales > 0

Is this a directional or nondirectional test?

Answer: __________________________

Explain why the hypotheses represent a directional or nondirectional test.

Do these hypotheses account for all possible values of the population mean difference?

Answer: __________________________

Explain how the null and alternative hypotheses divide the possible outcomes for the population mean difference.

Problem Set 3.4: Understanding p Values and Statistical Decisions

Criterion: Explain decisions based on p values.

A p value helps researchers determine whether the observed sample result provides sufficient evidence against the null hypothesis. The significance level, commonly represented by α, is established before conducting the statistical test.

Lambdin (2012) emphasized the importance of applying significance criteria consistently, stating, “If a p < .05 result is ‘significant,’ then a p = .067 result is not ‘marginally significant’” (p. 76).

Explain what this statement means in terms of the two possible statistical decisions a researcher can make.

Answer: __________________________

Your explanation should distinguish between:

Rejecting the null hypothesis.
Failing to reject the null hypothesis.

At α = .05, a p value below .05 generally provides sufficient evidence to reject the null hypothesis. A p value of .067 does not meet that predetermined significance criterion, so the researcher would fail to reject the null hypothesis.

Problem Set 3.5: One-Sample t Test in JASP

Criterion: Calculate and interpret a one-sample t test in JASP.

A one-sample t test determines whether the mean of a sample differs significantly from a known or hypothesized population mean.

Use the minutesreading.jasp dataset. The dataset contains the reading times, measured in minutes, of Riverbend City online news readers. Riverbend City Online News claims that its readers spend more time reading its content than readers spend with national news. The national-news population mean is 8 minutes per week.

Instructions for JASP

Download and open minutesreading.jasp in JASP. Then complete the following steps:

Select T-Tests from the toolbar.
Under Classical, select One-Sample T-Test.
Select Time and move it to the Variables box.
Make sure Student is selected.
Enter 8 in the Test Value field.
Run the analysis and review the output.
Copy and paste the JASP output into the Word document.

Then answer the following questions:

1. State the nondirectional hypothesis.

Answer: __________________________

2. What is the critical t value for α = .05 using a two-tailed test?

Answer: __________________________

The exact critical t value depends on the sample’s degrees of freedom.

3. Is the average reading time for Riverbend City Online News significantly different from the population mean of 8 minutes? Explain.

Answer: __________________________

Base your conclusion on the p value and the predetermined significance level.

Important: Keep the minutesreading.jasp dataset available because it will also be used for the confidence interval analysis.

Problem Set 3.6: Calculating a 95% Confidence Interval

Criterion: Calculate confidence intervals using JASP.

A confidence interval provides a range of plausible values for a population parameter based on sample data. A 95% confidence interval is commonly used to estimate the population mean while accounting for sampling uncertainty.

Continue using the minutesreading.jasp dataset and the one-sample t test from Problem Set 3.5.

In JASP:

Select Location Estimate.
Select Confidence Interval.
Enter 95.0% as the confidence level.
Review the resulting output.
Copy and paste the output into the Word document.

Report and interpret the 95% confidence interval in relation to the population mean of 8 minutes.

Problem Set 3.7: Independent-Samples t Test in JASP

Criterion: Calculate an independent-samples t test in JASP.

An independent-samples t test compares the means of two separate groups to determine whether their average scores differ significantly.

Use the scores.jasp dataset. Dr. Z wants to determine whether depression scores differ between clients who temporarily avoid watching or reading the news and clients who continue with therapy as usual.

Participants are divided into two groups. Group 1 is instructed not to watch or read news for two weeks while continuing therapy. Group 2 continues therapy as usual. Depression scores are measured after the two-week period.

Instructions for JASP

Download and open scores.jasp in JASP.
Select T-Tests from the toolbar.
Under Classical, select Independent-Samples T-Test.
Select Score and move it to the Dependent Variables box.
Select Group and move it to the Grouping Variable box.
Make sure Student is selected.
Select Descriptives.
Deselect any unnecessary options.
Review the output.
Copy and paste the JASP results into the Word document.

Problem Set 3.8: Interpreting an Independent-Samples t Test

Criterion: Identify the independent variable, dependent variable, and hypotheses and evaluate the null hypothesis for an independent-samples t test.

Use the information from Problem Set 3.7 to answer the following questions.

Identify the independent and dependent variables

Independent variable (IV): __________________________

Dependent variable (DV): __________________________

The independent variable is the condition assigned to the participants, while the dependent variable is the depression score measured after the two-week period.

State the hypotheses

Null hypothesis (H₀): __________________________

Directional alternative hypothesis (H₁): __________________________

The directional hypothesis should reflect the expected direction of the difference between the two groups.

Evaluate the null hypothesis

Can the null hypothesis be rejected at α = .05?

Answer: __________________________

Explain your decision using the appropriate JASP test result and p value. If the p value is less than .05, reject the null hypothesis. If the p value is greater than or equal to .05, fail to reject the null hypothesis.

Problem Set 3.9: Independent-Samples t Test Using Excel

Criterion: Calculate an independent-samples t test in Excel.

Excel can be used to conduct an independent-samples t test when comparing the means of two independent groups. In this exercise, you will perform the analysis twice: once assuming equal variances and once assuming unequal variances.

Depression Score Data

Group 1: 34, 25, 4, 64, 14, 49, 54

Group 2: 24, 78, 59, 68, 84, 79, 57

Conducting the Equal-Variance t Test

Open Microsoft Excel and enter the data into an empty worksheet.

Place the group labels at the top:

Cell A1: 1
Cell B1: 2

Enter the Group 1 scores below the first label and the Group 2 scores below the second label.

Then:

Select Data Analysis.
Choose t-Test: Two-Sample Assuming Equal Variances.
Select OK.
For Variable 1 Range, enter $A$2:$A$8.
For Variable 2 Range, enter $B$2:$B$8.
Run the analysis.
Review the results that Excel places on a new worksheet.

Copy the complete output into the Word document.

Conducting the Unequal-Variance t Test

Return to the original data worksheet and select Data Analysis again.

Choose t-Test: Two-Sample Assuming Unequal Variances and select OK.

Enter:

Variable 1 Range: $A$2:$A$8

Variable 2 Range: $B$2:$B$8

Run the analysis and review the results on the new worksheet.

Copy the results into the Word document.

Compare the results from the equal-variance and unequal-variance tests. Pay particular attention to the calculated t statistic, degrees of freedom, and p value when interpreting whether the two groups differ significantly.

Key Concepts to Remember

Hypothesis testing begins with a null hypothesis and an alternative hypothesis. The researcher uses sample data to determine whether there is enough statistical evidence to reject the null hypothesis.

Effect size and statistical power answer different questions. Effect size describes how large a difference or relationship is, whereas power describes the probability of detecting a true effect through a statistical test.

A one-sample t test compares one sample mean with a known or hypothesized population mean. An independent-samples t test compares the means of two separate groups. Confidence intervals provide an estimated range of plausible population values and help communicate the precision of a sample estimate.

When interpreting p values, researchers should use the significance level established before the analysis. Statistical significance should not be determined by labeling results that fall just above the chosen threshold as “marginally significant.”

Frequently Asked Questions

What is a hypothesis test?

A hypothesis test is a statistical procedure used to evaluate whether sample data provide enough evidence to reject a null hypothesis about a population.

What is the difference between a null hypothesis and an alternative hypothesis?

The null hypothesis generally states that there is no difference, relationship, or effect. The alternative hypothesis represents the research expectation that a difference, relationship, or effect exists.

What is statistical power?

Statistical power is the probability that a statistical test will correctly detect an effect when a genuine effect exists. Larger samples, larger effect sizes, and lower variability generally increase statistical power.

What does effect size mean?

Effect size indicates the magnitude of a difference or relationship. Unlike a p value, which addresses statistical evidence, effect size provides information about the practical or substantive size of an effect.

What is the difference between a one-tailed and two-tailed test?

A one-tailed test is used when the alternative hypothesis predicts a specific direction of an effect. A two-tailed test is used when the researcher predicts a difference but does not specify its direction.

What does a p value of less than .05 mean?

When the significance level is set at α = .05, a p value below .05 generally indicates sufficient statistical evidence to reject the null hypothesis. It does not mean that there is a 95% probability that the research hypothesis is true.

What is a 95% confidence interval?

A 95% confidence interval provides a range of values estimated from sample data that is intended to capture the population parameter with a specified long-run confidence level.

What is a one-sample t test used for?

A one-sample t test evaluates whether a sample mean differs significantly from a specified population or hypothesized mean.

What is an independent-samples t test?

An independent-samples t test determines whether the means of two independent groups differ significantly.

Why are both equal-variance and unequal-variance t tests performed in Excel?

The two procedures make different assumptions about the population variances. The equal-variance test assumes that the two populations have the same variance, while the unequal-variance procedure, commonly associated with Welch’s t test, does not require that assumption.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). American Psychological Association. https://apastyle.apa.org/products/publication-manual-7th-edition

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863