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PSYC FPX 4700 Assessment 4 Anova Chi Square Tests and Regression

Student Name

Capella University

PSYC FPX 4700 Statistics for the Behavioral Sciences

Prof. Name:

Date

Problem Set 4.1: Critical Value

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 Significancek = 2k = 4k = 6k = 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.

Problem Set 4.2: One-way ANOVA in JASP

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.

  1. Download stress.jasp. Double-click the icon to open the dataset in JASP.
  2. In the Toolbar, click ANOVA. From the menu that appears, select ANOVA under Classical.
  3. Select Fat grams consumed and click the upper Arrow to move it to the Dependent Variable box.
  4. Select Stress level and click the lower Arrow to move it to the Fixed factors box.
  5. Check the Descriptive statistics box.
  6. Copy and paste the output below.

Problem Set 4.3: One-way ANOVA in Excel

Criterion: Calculate an ANOVA in Excel.

Instructions: Use the data from the table below to complete the following steps:

Stress LevelsHighModerateLow
 10997
 4487
 61265
 687
  1. In Row 1, enter High in cell A1, Moderate in cell B1, and Low in cell C1.
  2. In the toolbar, click Data Analysis, select Anova: Single Factor, and click OK.
  3. In Input Range: $A$1:$C$6, check the box next to Labels in First Row, then click OK.
  4. Results will appear in a new sheet to the left; copy and paste the output below.

Problem Set 4.4: One-way ANOVA Results in APA Style

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). ___

Problem Set 4.5: Interpret ANOVA Results

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 VariablesLife SatisfactionMSDFp
Sex 0.68.409  
Men3.990.51   
Women3.940.49   
Age 3.04.029  
20s3.850.42   
30s4.030.52   
40s3.970.57   
50s4.020.50   
Marital status 12.46.000  
Single3.850.48   
Married4.100.50   
Divorced4.000.35   
Education 0.82.536  
High school3.920.48   
Postsecondary3.850.54   
University degree4.000.51   
Masters4.000.59  

Which factors were significant at the .05 level of significance? _ State the number of levels for each factor. __

Problem Set 4.6: Tukey HSD Test in JASP

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).

  1. Download stress.jasp. Double-click the icon to open the dataset in JASP.
  2. In the Toolbar, click ANOVA. From the menu that appears, select ANOVA under Classical.
  3. Select Fat grams consumed and click the upper Arrow to move it to the Dependent Variable box.
  4. Select Stress level and click the lower Arrow to move it to the Fixed factors box.
  5. Check the Descriptive statistics box.
  6. Select Post-Hoc Tests. In the menu that appears, select Stress level and click the Arrow to move it from the left to the right box.
  7. Check Standard and Tukey and uncheck any other boxes in the Post-Hoc area.
  8. Copy and paste the output below.

Note: You will use these results for Problem Set 4.7.

Problem Set 4.7: Tukey HSD Interpretation

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.

Chi-Square Tests

Problem Set 4.8: Critical Values

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 Significancek = 10k = 16k = 22k = 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. ___

Problem Set 4.9: Parametric Tests

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. ___

Problem Set 4.10: Chi-Square Analysis in JASP

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.

  1. Download yummy.jasp. Double-click the icon to open the dataset in JASP.
  2. In the Toolbar, click Frequencies. From the menu that appears, select Multinomial Test under Classical.
  3. Select Flavor and click the upper Arrow to move it to the Factor box.
  4. Select Frequency and click the lower Arrow to move it to the Counts box.
  5. Click the circle next to Expected Proportions (χ2).
  6. Enter 4 for Chocolate, 3 for Vanilla, and 1 for Strawberry.
  7. Check the box for Descriptives and click the circle next to Proportions.
  8. Copy and paste the output into the Word document.

Answer this: Was Tandy’s distribution of proportions the same as expected?

Regression

Problem Set 4.11: Analysis of Regression in JASP

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.

  1. Download satisfaction.jasp. Double-click the icon to open the dataset in JASP.
  2. In the Toolbar, click Regression. From the menu that appears, select Linear regression under Classical.
  3. Select Life Satisfaction and click the upper Arrow to move it to the Dependent box.
  4. Set Method to “Enter.”
  5. Select Age and click the Arrow to move it to the Covariates box.
  6. Under Statistics, select Descriptives, Estimates, and Model Fit, and deselect all other boxes.
  7. Copy and paste the output into this Word document.

Problem Set 4.12: Analysis of Regression in Excel

Criterion: Use Excel to complete an analysis of regression.

Data: Use the data from the table below.

X (Age in Years)Y (Life Satisfaction)
186
188
267
285
329
198
215
206
257
429

Instructions:

  1. Open Excel and work in a new sheet.
  2. Enter the data from the table in Problem Set 4.11. Label Cell A1 as X and Cell B1 as Y, then enter the data below.
  3. In the toolbar, click Data Analysis and select Regression.
  4. Check the boxes for Labels and Confidence Level.
  5. In Input Y Range: $B$1:$B$11, and in Input X Range: $A$1:$A$11.
  6. Click OK. Your data will appear in a new sheet to the left.
  7. Copy and paste the output into this document.

Problem Set 4.13: Identify Tests for Ordinal Data

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.

PSYC FPX 4700 Assessment 4 Anova Chi Square Tests and Regression

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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