Graded Essays

ANOVA, Chi-Square Tests, and Regression

Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.

ANOVA

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. 

Work through the following and write down what you see in the F-table. This will help familiarize you with the table. 

The F-table: The degrees of freedom for the numerator (k − 1) are across the columns; the degrees of freedom for the denominator (N − k) are across the rows in the table. A separate table is included for a .05 and .01 level of significance. 

Increasing the levels of the independent variable (k):

Suppose we have a sample size of 24 participants (N = 24). Record the critical values given the following values for k:

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.

PSYC FPX4700 Assessment 4 ANOVA, Chi-Square Tests, and Regression

As the number of groups (k) increases from 1 to 8, the critical F-value shows a decreasing trend. This implies that the F-statistic needed to reject the null hypothesis decreases with the increase in groups. The reason behind this is that when the number of groups is more, the difference in means among them can be better clarified by the treatment effect, which reduces the likelihood of finding a significant difference by chance alone.

On the other hand, the decreasing critical F-value implies that as the number of groups (k) increases, the power of the test to detect a significant difference between group means also decreases. Power refers to the probability of accurately rejecting the null hypothesis when it is actually false, and it is affected by various factors, including sample size, effect size, and significance level. As k rises, the degrees of freedom for the denominator also decrease, which minimizes the overall data variability and may decrease the test’s power. As a result, the relationship between k and power is not straightforward and is influenced by other factors such as sample size and effect size.

Problem Set 4.2: One-way ANOVA in JASP

Criterion: Calculate an ANOVA in JASP.

Data: Use the dataset stress.jasp.The dataset stress.jasp is a record of the amount of fat (in grams) consumed in 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. In the menu that appears, under Classical, select ANOVA.
3. Select Fat grams consumed and then click the upper Arrow to send it over to the Dependent Variable box.
4. Select Stress level and then click the lower Arrow to send it over to the Fixed factors box.
5. Check the Descriptive statistics box. 
6. Copy and paste the output below.

ANOVA

Descriptives

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:

1. Open Excel to an empty sheet.
2. Enter the data from this table.

1. In Row 1, enter High in cell A1, Moderate in cell B1, and Low in cell B1.
2. In the toolbar, click Data Analysis, select Anova: Single Factor, and click OK.
3. In Input Range: $A$1:$C$6, put a check next to Labels in First Row, click OK.
4. Results will appear in a new sheet to the left; copy and paste the input 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 4.4.

Instructions: Complete the following:

1. State the null hypothesis. _______ No relationship between stress and fat consumption exists.
2. Report your results in APA format (as you might see them reported in a journal article). _  

A one-way ANOVA was performed with high, medium, and low-stress levels as the independent variable and fat consumption as the dependent variable. The analysis did not yield sufficient evidence to conclude a relationship between stress and fat consumption. Participants in the medium and low-stress groups reported lower fat consumption levels than those in the high-stress group. Interestingly, there was no significant difference in fat consumption between the medium and low-stress groups, suggesting that stress may not be a crucial factor in determining fat consumption levels._______

PSYC FPX4700 Assessment 4 ANOVA, Chi-Square Tests, and Regression

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) tested differences in life satisfaction among sport coaches. They tested differences by sex, age, marital status, and education. The results of each test in the following table are similar to the way in which the data were given in their article.

1. Which factors were significant at a .05 level of significance? _______ 

According to the provided results, age and marital status were found to be significant factors at a .05 level of significance, with p-values less than .05. In contrast, sex and education were not significant, as their p-values were greater than .05. These findings suggest that age and marital status may play a crucial role in the outcome variable, while sex and education may not have a significant effect.

1. State the number of levels for each factor. __The number of levels for sex =2, for age = 4, for marital status= 3 and education =04___

Problem Set 4.6: Tukey HSD Test in JASP

Criterion: Calculate post hoc analyses in JASP.

Data: Use 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. In the menu that appears, under Classical, select ANOVA.
3. Select Fat grams consumed and then click the upper Arrow to send it over to the Dependent Variable box.
4. Select Stress level and then click the lower Arrow to send it over 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 then 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.

ANOVA

Descriptives

Post Hoc Tests

Standar