PSYC FPX 4700 Assessment 3 Hypothesis Effect Size Power and Tests

PSYC FPX 4700 Assessment 3 Hypothesis Effect Size Power and Tests

Student Name

Capella University

PSYC FPX 4700 Statistics for the Behavioral Sciences

Prof. Name:

Date

Hypothesis Effect Size Power and Tests

Work through the problems listed below in this Word document. Do not submit any additional files. Provide examples of your work for problem sets requiring calculations. Make sure your solution to each problem is easy to see. To differentiate your response, you might want to highlight it or use a different typeface color.

Criterion: Interpret population mean and variance.

Instructions: Answer the questions after reading the information below.

Assume a scientist needs to conduct a more in-depth study of the mean focusing ability of individuals in a hypothetical population. The following characteristics are cited by the researcher as evidence of a normal distribution of attention span—the amount of time spent on a given task in minutes—in this population: 20 and 36. Provide responses to the following questions based on the parameters presented in this example:

What is the mean population size (μ)? 20 minutes: What is the variance in the population? Draw a map of this population’s distribution in 36 minutes. Label the mean plus and minus three standard deviations and draw the distribution’s shape.

Standard deviation of the population = σ = 36 = 6

μ – 3σ = 20 – (3 × 6) = 2

μ – 2σ = 20 – (2 × 6) = 8

μ – σ = 20 – 6 = 14

μ + σ = 20 + 6 = 26

μ + 2σ = 20 + (2 × 6) = 32

μ + 3σ = 20 + (3 × 6) = 38

PSYC FPX 4700 Assessment 3 Hypothesis, Effect Size, Power, and t Tests

Problem Set 3.2: Effect Size and Power

Criterion: Explain effect size and power.

Instructions: Read each of the three scenarios below and respond to the questions.

A test designed by two researchers measures the efficacy of drug treatment. According to Researcher A, the effect size for the male population is d = 0.36; Scientist B confirms that the effect size for the female population is d = 0.20. If all other factors are equal, which researcher has a greater ability to identify an effect? Explain.

Researcher A is likely to have a higher ability to identify the effect due to the larger disparity between the null and alternative means. This is because the test is more powerful with a larger effect size.

Two researchers conduct a study on the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (n = 22), while Researcher B gathers a sample of 40 married couples (n = 40). All other factors being equal, which researcher has a greater ability to detect an effect? Explain.

Researcher B has a greater ability to detect an effect due to the larger sample size, as power is positively correlated with sample size.

Two researchers conduct a study on standardized test performance among high school students in two nearby communities. Researcher A tests performance in the northern community, where the standard deviation of scores is 110 (σ); Researcher B tests performance in the southern community, where the standard deviation of scores is 60 (σ). If all other factors are equal, which researcher has a greater ability to identify an effect? Explain.

Researcher B has a greater ability to detect an effect due to the smaller standard deviation, which typically indicates less variability in scores and thus a clearer signal of any potential effect.

Problem Set 3.3: Hypothesis, Direction, and Population Mean

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

Instructions: Read the following and answer the questions.

Testing hypotheses in a directional or nondirectional manner. A commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research was provided by Cho and Abe (2013). To test a research hypothesis that males self-disclose more than females, they discussed the following hypothetical null and alternative hypotheses:

H0: Males = Females
H1: Males > Females

Which type of test is used to test these hypotheses? A directional or nondirectional test?

Since the alternative hypothesis (H1) is stated in a way that specifies a single direction of effect—indicating that males engage in greater self-disclosure than females—the hypothesis is formulated as a directional test.

Do these hypotheses encompass all population mean possibilities? Explain.

The provided hypotheses account for all potential outcomes regarding the population mean. Since male means can be equal to, lower than, or higher than female means, the hypotheses cover every possible scenario for the population mean.

Problem Set 3.4: Hypothesis, Direction, and Population Mean

Criterion: Explain decisions for p values.

Instructions: Review the following and answer the brief.

The value of a p value. In a straightforward commentary on the use of significance testing, Lambdin (2012) explained, “If a p < .05 result is ‘significant,’ a p = .067 result is not ‘insignificantly significant’” (p. 76).

Identify the two options available to a researcher and explain what the author is referring to.

A researcher will reject the null hypothesis if the p-value is less than 0.05, while they will fail to reject the null hypothesis and accept the alternative hypothesis if the p-value is greater than 0.05.

t Tests

Problem Set 3.5: One-Sample t test in JASP

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

Data: Utilize the minutesreading.jasp dataset. This dataset contains a sample of reading times (in minutes) for Riverbend City online news readers. Riverbend City online news claims that it is read longer than public news, which has a mean reading time of 8 minutes per week.

Instructions: Complete the steps below.

The minutesreading.jasp dataset can be downloaded. To open the dataset in JASP, double-click the icon.

1. Click on T-tests in the Toolbar. Select One-sample t-test from the Classical menu that appears.
2. Select Time and click the Arrow to move it to the Variables box.
3. Ensure the box is checked for Student. Enter 8 into the box labeled “Test value.” Press enter.
4. Copy and paste the output into the Word document.

One Sample T-Test

Note: For the Student t-test, the alternative hypothesis specifies that the mean is different from 8.

Be specific about the nondirectional hypothesis.

The mean viewing time for Riverbend City online news differs from the public news mean of 8 minutes per week in the population.

For α = .05 (two tails), specify the critical t.

If df = 14 and α = .05 (two tails) are used, the critical t is 2.145. Is Riverbend City’s online news viewing duration significantly different from the population mean? Explain.
With a t-value of -0.493 and a p-value of 0.629, we were unable to reject the null hypothesis that the population mean viewing time for Riverbend City online news is the same as the national mean of 8 minutes per week. The p-value exceeds the established significance level (α = 0.05). Therefore, we cannot conclude that Riverbend City online news viewing duration significantly differs from the population mean.

Note: You will continue to use this dataset for the next problem.

Problem Set 3.6: Confidence Intervals

Criterion: Calculate confidence intervals using JASP.

Data: Continue using the minutesreading.jasp dataset.

Instructions: Follow the steps below to calculate the 95% confidence interval using the output from Problem Set 3.5, which includes a test value (population mean) of 8.

1. Check the box next to Location Estimate.
2. Review the Confidence Interval box. Check the box for 95.0 percent.
3. Copy the output into the Word document.

One Sample T-Test

Note: For the Student t-test, the mean difference estimate is given by the sample mean difference d.
Note: For the Student t-test, the alternative hypothesis specifies that the mean is different from 8.
Note: Student’s t-test.

Problem Set 3.7: Independent Samples t Test

Criterion: Calculate an independent samples t test in JASP.

Data: Use the scores.jasp dataset. Dr. Z wants to determine if individuals who do not watch or read the news have lower depression scores than those who continue with their usual therapy. She divides her depressed patients into two groups. Group 1 is instructed not to watch or read any news during treatment, while Group 2 continues with their usual treatment. After two weeks, the measure’s results are recorded in the scores.jasp dataset.

Instructions: Complete the steps below.

1. Obtain the scores.jasp dataset. To open the dataset in JASP, double-click the icon.
2. Click on T-tests in the Toolbar. Select Independent-samples T-test under Classical from the menu that appears.
3. Move Score to the Dependent Variables box by clicking the top Arrow after selecting it.
4. Select Group and then click the bottom Arrow to move it to the Group Variable box.
5. Ensure that the Student checkbox is selected. Deselect any other boxes and select Descriptives as well.
6. Copy the output into the Word document.

Independent Samples T-Test

Note: Student’s t-test.

Problem Set 3.8: Independent t Test in JASP

Criterion: Identify IV, DV, and hypotheses and evaluate the null hypothesis for an independent samples t test.

Data: Use the information from Problem Set 3.7.

Instructions: Complete the following:

In the study, identify the IV and DV.

IV: Group (news abstention versus normal therapy);
DV: Depression scores.

Indicate both the directional (one-tailed) alternative hypothesis and the null hypothesis for the depression scores.

Null hypothesis: There is no significant difference in depression scores between individuals who abstain from watching news and those who continue with treatment as usual.

Alternative hypothesis: Individuals who do not watch the news have significantly different depression scores compared to those who continue with therapy as usual.

Can you reject the null hypothesis at α = .05? Provide a rationale.

PSYC FPX 4700 Assessment 3 Hypothesis Effect Size Power and Tests

The null hypothesis can be rejected at α = .05. Typically, the null hypothesis posits that the means of the two independent groups being compared do not significantly differ. In this case, the negative t-value (-2.580) indicates that the mean for Group 1 is lower than that for Group 2. The alpha level of 0.05 is less than the p-value of 0.024.

When the p-value is less than the alpha level, it suggests that the likelihood of observing such a substantial difference between the groups by chance alone is less than 5%. In other words, there is strong evidence that the difference between the two groups is not merely due to random variation.

Therefore, based on these results, we can reject the null hypothesis and conclude that there is a significant difference between the means of the two independent groups being examined.

Problem Set 3.9: Independent t Test using Excel

Criterion: Calculate an independent samples t test in Excel.

Data: Use the following data:

Depression Scores:

Group 1: 34, 25, 4, 64, 14, 49, 54
Group 2: 24, 78, 59, 68, 84, 79, 57

Instructions: Complete the following steps:

1. Open Excel.
2. Enter the data from above in a new tab. Use column A for Group 1 and column B for Group 2. Enter 1 in Cell A1 and 2 in Cell B1.
3. Below the labels, input the data for each group.
4. Select t-Test by clicking on Data Analysis: Two-Sample Assuming Equal Variances. Click OK.
5. Enter $A$2:$A$8 into Variable 1 Range. Alternatively, you can highlight your data for Group 1 by clicking the graph icon to the right of the box.
6. Enter $B$2:$B$8 into the Variable 2 Range field.
7. Click OK. A new tab will open with your results.
8. Return to your files. Select t-Test by clicking on Data Analysis: Two-Sample Assuming Unequal Variances. Click OK.
9. Enter $A$2:$A$8 into Variable 1 Range. Alternatively, click the graph icon to the right of the box and highlight your data for Group 1.
10. In Variable 2 Range, enter $B$2:$B$8.
11. Click OK. A new tab will open with your results.
12. Below, copy the results of the two t-tests.

T-Test: Two-Sample Assuming Equal Variances

T-Test: Two-Sample Assuming Unequal Variances