Student Name
Capella University
PSYC FPX 4700 Statistics for the Behavioral Sciences
Prof. Name:
Date
Criterion: Explain the relationship between k and power based on calculated k values.
Instructions: Read the following and answer the questions.
Familiarize yourself with the F-table by working through the following.
The F-table: The degrees of freedom for the numerator (k − 1) are represented across the columns, while the degrees of freedom for the denominator (N − k) are displayed across the rows in the table. Separate tables are provided for significance levels of .05 and .01.
Increasing the levels of the independent variable (k): Assume a sample size of 24 participants (N = 24). Record the critical values for the following k values:
Level of Significance | k = 2 | k = 4 | k = 6 | k = 8 |
---|---|---|---|---|
.05 | ___ | ___ | ___ | ___ |
.01 | ___ | ___ | ___ | ___ |
As k increases (from 1 to 8), does the critical value increase or decrease? Based on your answer, explain how k is related to power.
Criterion: Calculate an ANOVA in JASP.
Data: Use the dataset stress.jasp. This dataset records the amount of fat (in grams) consumed during a buffet-style lunch among professional bodybuilders under conditions of high, moderate, and low stress.
Instructions: Complete the steps below.
Criterion: Calculate an ANOVA in Excel.
Instructions: Use the data from the table below to complete the following steps:
Stress Levels | High | Moderate | Low | |
---|---|---|---|---|
10 | 9 | 9 | 7 | |
4 | 4 | 8 | 7 | |
6 | 12 | 6 | 5 | |
6 | 8 | 7 |
Criterion: Report ANOVA results in APA format.
Data: Use the results from Problem Set 4.3.
Instructions: Complete the following:
State the null hypothesis. ___
Report your results in APA format (as you might see them reported in a journal article). ___
Criterion: Interpret the results of an ANOVA.
Instructions: Read the following and answer the question.
Data: Life satisfaction among sport coaches. Drakou et al. (2006) examined differences in life satisfaction among sport coaches based on sex, age, marital status, and education. The results of each test are summarized in the following table, similar to how the data were presented in their article.
Independent Variables | Life Satisfaction | M | SD | F | p |
---|---|---|---|---|---|
Sex | 0.68 | .409 | |||
Men | 3.99 | 0.51 | |||
Women | 3.94 | 0.49 | |||
Age | 3.04 | .029 | |||
20s | 3.85 | 0.42 | |||
30s | 4.03 | 0.52 | |||
40s | 3.97 | 0.57 | |||
50s | 4.02 | 0.50 | |||
Marital status | 12.46 | .000 | |||
Single | 3.85 | 0.48 | |||
Married | 4.10 | 0.50 | |||
Divorced | 4.00 | 0.35 | |||
Education | 0.82 | .536 | |||
High school | 3.92 | 0.48 | |||
Postsecondary | 3.85 | 0.54 | |||
University degree | 4.00 | 0.51 | |||
Masters | 4.00 | 0.59 |
Which factors were significant at the .05 level of significance? _ State the number of levels for each factor. __
Criterion: Calculate post hoc analyses in JASP.
Data: Use the stress.jasp data from Problem Set 4.2.
Instructions: Complete the steps below. (Note: The first 7 steps below are repeated from Problem Set 4.2).
Note: You will use these results for Problem Set 4.7.
Criterion: Interpret Tukey HSD results from JASP output.
Data: Use your output from Problem Set 4.6.
Instructions: Identify where significant differences exist at the .05 level between the stress levels.
Criterion: Explain changes in critical value based on calculations.
Instructions: Read the following and answer the questions.
The chi-square table: The degrees of freedom for a given test are listed in the far-left column, while the level of significance is displayed in the top row to the right. These are the only two values needed to find the critical values for a chi-square test.
Familiarize yourself with the chi-square table by working through the following exercise.
Increasing k and α in the chi-square table: Record the critical values for a chi-square test, given the following values for k at each level of significance:
Level of Significance | k = 10 | k = 16 | k = 22 | k = 30 |
---|---|---|---|---|
.10 | ___ | ___ | ___ | ___ |
.05 | ___ | ___ | ___ | ___ |
.01 | ___ | ___ | ___ | ___ |
As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain. ___
As k increases (from 10 to 30), does the critical value increase or decrease? Explain your answer in relation to the test statistic. ___
Criterion: Identify parametric tests.
Instructions: Based on the scale of measurement for the data, identify whether a test is parametric or nonparametric.
A researcher measures the proportion of schizophrenic patients born in each season. ___
A researcher measures the average age at which schizophrenia is diagnosed among male and female patients. ___
A researcher tests whether the frequency of Internet use and social interaction are independent. ___
A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes. ___
Criterion: Use JASP for a chi-square analysis.
Data: Use the dataset yummy.jasp. Tandy’s ice cream shop serves chocolate, vanilla, and strawberry ice cream. Tandy wants to plan for future years and expects to purchase 100 cases of chocolate, 75 cases of vanilla, and 25 cases of strawberry (4:3:1). This year, she purchased 133 cases of chocolate, 82 cases of vanilla, and 33 cases of strawberry. The dataset yummy.jasp records ice cream sales for this year.
Instructions: Complete the steps below.
Answer this: Was Tandy’s distribution of proportions the same as expected?
Criterion: Use JASP to complete an analysis of regression to determine if the variable age is a predictor of the variable life satisfaction.
Data: Use the dataset satisfaction.jasp. This dataset contains responses to a survey in which participants of various ages rated their level of life satisfaction on a 1–10 scale, with 1 being “very dissatisfied” and 10 being “completely satisfied.”
Instructions: Complete the steps below.
Criterion: Use Excel to complete an analysis of regression.
Data: Use the data from the table below.
X (Age in Years) | Y (Life Satisfaction) |
---|---|
18 | 6 |
18 | 8 |
26 | 7 |
28 | 5 |
32 | 9 |
19 | 8 |
21 | 5 |
20 | 6 |
25 | 7 |
42 | 9 |
Instructions:
Criterion: Identify tests for ordinal data.
Instructions: Read the following and answer the questions.
Identify the appropriate nonparametric test for each of the following examples and explain why a nonparametric test is appropriate.
A researcher measures fear as the time it takes to walk across a presumably scary portion of campus. The times (in seconds) that it took a sample of 12 participants were 8, 12, 15, 13, 12, 10, 6, 10, 9, 15, 50, and 52. ___
For this scenario, the appropriate nonparametric test is the Wilcoxon Signed-Rank Test. This test is suitable because the data is ordinal, and the sample size is small. The Wilcoxon Signed-Rank Test assesses whether there is a significant difference between the median of the sample and a specified value, which is appropriate for the ranking of times taken by participants.
Two groups of participants were given 5 minutes to complete a puzzle. The participants were told that the puzzle would be easy. In truth, one group had a solution (Group Solution), while the second group had no solution (Group No Solution). The researchers measured stress levels and found that frustration levels were low for all participants in Group Solution and for all but a few participants who exhibited significantly high levels of stress in Group No Solution. ___
In this case, the Mann-Whitney U Test is the appropriate nonparametric test. This test is suitable because it compares the ranks of two independent groups. Since the stress levels are ordinal and the groups are independent, the Mann-Whitney U Test can effectively determine if there is a significant difference in stress levels between the two groups.
A researcher measured student scores on an identical assignment to see how well students perform for different types of professors. In Group Adviser, their professor was also their adviser; in Group Major, their professor taught in their major field of study; and in Group Nonmajor, their professor did not teach in their major field of study. Student scores were ranked in each class, and the differences in ranks were compared. ___
The Kruskal-Wallis H Test is the appropriate nonparametric test for this scenario. This test is used to compare the ranks of three or more independent groups. Since the data is ordinal and involves multiple groups of students, the Kruskal-Wallis H Test can determine if there are significant differences in student performance across the different types of professors.
A researcher has the same participants rank two types of advertisements for the same product. Differences in ranks for each advertisement were compared. ___
For this situation, the Wilcoxon Signed-Rank Test is again the appropriate nonparametric test. This test is suitable because it compares the ranks of two related samples. Since the same participants are ranking both advertisements, the Wilcoxon Signed-Rank Test can effectively assess whether there is a significant difference in the rankings of the two types of advertisements.
A professor measures student motivation before, during, and after a statistics course in a given semester. Student motivation was ranked at each time in the semester, and the differences in ranks were compared. ___
In this case, the Friedman Test is the appropriate nonparametric test. This test is used for comparing three or more related groups. Since the same participants are being measured at three different times (before, during, and after the course), the Friedman Test can determine if there are significant differences in student motivation across these time points.
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.
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