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

PSYC FPX 4700 Assessment 4 Anova Chi Square Tests and Regression

ANOVA, chi-square tests, and regression are widely used statistical methods for analyzing relationships, differences, and patterns in research data. ANOVA is primarily used to compare the means of three or more groups, chi-square tests examine categorical data and observed versus expected frequencies, and regression determines whether one or more variables can predict an outcome. In this assessment, you will practice these statistical methods using F-tables, chi-square critical values, JASP, Excel, APA-style reporting, and interpretation of statistical results.

Complete all problems in this Word document. Do not submit additional files. For questions that require calculations, show your work clearly. Make sure each final answer is easy to identify. You may highlight your answers or use a different font color to distinguish them from your calculations and explanations.

ANOVA

Analysis of variance (ANOVA) is a statistical procedure used to determine whether statistically significant differences exist among the means of multiple groups. A one-way ANOVA examines the effect of one independent variable with two or more levels on a continuous dependent variable.

Problem Set 4.1: ANOVA Critical Values

Criterion: Explain the relationship between the number of levels of an independent variable (k) and statistical power using calculated critical values.

Review the F-distribution table and answer the questions below. This exercise is designed to help you become familiar with locating critical values in an F-table.

In an F-table, the degrees of freedom for the numerator, calculated as k − 1, are displayed across the columns. The degrees of freedom for the denominator, calculated as N − k, are displayed across the rows. Separate tables are generally provided for different significance levels, including α = .05 and α = .01.

Increasing the Number of Independent-Variable Levels

Assume a sample contains 24 participants (N = 24). Determine the appropriate critical F value for each value of k below.

Number of Levels (k)	Critical F at α = .05	Critical F at α = .01
k = 2
k = 4
k = 6
k = 8

After completing the table, answer the following:

As k increases from 1 to 8, does the critical F value generally increase or decrease? Explain how changes in the number of levels of the independent variable are related to statistical power.

Problem Set 4.2: One-Way ANOVA Using JASP

Criterion: Conduct a one-way ANOVA using JASP.

Data: Use the stress.jasp dataset. The dataset contains information about the amount of fat, measured in grams, consumed during a buffet-style lunch by professional bodybuilders experiencing high, moderate, or low levels of stress.

Open the stress.jasp dataset in JASP and complete the following procedure:

1. Download the stress.jasp file and open it in JASP.
2. Select ANOVA from the toolbar.
3. Under Classical, select ANOVA.
4. Select Fat grams consumed and move it to the Dependent Variable field.
5. Select Stress level and move it to the Fixed Factors field.
6. Select Descriptive statistics.
7. Copy and paste the resulting JASP output into the Word document.

Problem Set 4.3: One-Way ANOVA Using Excel

Criterion: Conduct a one-way ANOVA using Microsoft Excel.

Use the following data to perform a one-way ANOVA.

High Stress	Moderate Stress	Low Stress
10	9	9
7	4	4
8	7	6
12	6	5
6	8	7

Complete the following steps:

1. Open a new Excel worksheet.
2. Enter the data into three columns.
3. Enter High in cell A1, Moderate in cell B1, and Low in cell C1.
4. Select Data Analysis from the Excel toolbar.
5. Choose ANOVA: Single Factor and select OK.
6. For the input range, enter $A$1:$C$6.
7. Select Labels in First Row.
8. Run the analysis.
9. Excel will place the ANOVA results in a new worksheet.
10. Copy and paste the results into this Word document.

Problem Set 4.4: Reporting One-Way ANOVA Results in APA Style

Criterion: Report ANOVA findings using APA style.

Use the ANOVA results from the preceding analysis to complete the following:

State the null hypothesis.

Report the ANOVA results in APA format as they might appear in a peer-reviewed journal article.

Your report should clearly identify the test statistic, degrees of freedom, p value, and whether the findings are statistically significant.

Problem Set 4.5: Interpreting ANOVA Results

Criterion: Interpret ANOVA findings and determine which factors are statistically significant.

Drakou et al. (2006) examined life satisfaction among sport coaches. The researchers investigated whether life satisfaction differed according to sex, age, marital status, and education. The results are presented below.

Independent Variable	Group	M	SD	F	p
Sex	Men	3.99	0.51	0.68	.409
	Women	3.94	0.49
Age	20s	3.85	0.42	3.04	.029
	30s	4.03	0.52
	40s	3.97	0.57
	50s	4.02	0.50
Marital Status	Single	3.85	0.48	12.46	< .001
	Married	4.10	0.50
	Divorced	4.00	0.35
Education	High school	3.92	0.48	0.82	.536
	Postsecondary	3.85	0.54
	University degree	4.00	0.51
	Master’s	4.00	0.59

Using an alpha level of .05, answer the following questions:

1. Which independent variables produced statistically significant results?
2. How many levels does each independent variable contain?

Explain your answers using the reported F values and p values.

Problem Set 4.6: Tukey HSD Post Hoc Test in JASP

Criterion: Conduct and report a post hoc analysis using JASP.

Data: Use the stress.jasp dataset from Problem Set 4.2.

Repeat the initial ANOVA procedure and then complete the following:

1. Open stress.jasp in JASP.
2. Select ANOVA from the toolbar.
3. Under Classical, select ANOVA.
4. Move Fat grams consumed to the Dependent Variable field.
5. Move Stress level to the Fixed Factors field.
6. Select Descriptive statistics.
7. Select Post-Hoc Tests.
8. Move Stress level into the post hoc analysis field.
9. Select Standard and Tukey.
10. Deselect any unnecessary post hoc options.
11. Copy and paste the resulting output into the Word document.

Keep this output available because you will use it to complete Problem Set 4.7.

Problem Set 4.7: Interpreting the Tukey HSD Test

Criterion: Interpret Tukey HSD results generated by JASP.

Use the output from Problem Set 4.6 to determine which pairs of stress levels show statistically significant differences at the .05 significance level.

Identify the specific group comparisons that are significant and explain what the findings mean in relation to fat consumption.

Chi-Square Tests

Chi-square tests are commonly used when researchers analyze categorical variables. A chi-square goodness-of-fit test compares observed frequencies with expected frequencies, while a chi-square test of independence evaluates whether two categorical variables are associated.

Problem Set 4.8: Chi-Square Critical Values

Criterion: Explain how critical values change based on degrees of freedom and significance level.

Review the chi-square distribution table before answering the questions.

In a chi-square table, the degrees of freedom (df) are listed in the far-left column, while the significance levels are displayed across the top of the table. These values are used to locate the appropriate critical value.

For a goodness-of-fit test, calculate degrees of freedom using:

df = k − 1

Complete the following table.

k	α = .10	α = .05	α = .01
10
16
22
30

Answer the following questions:

1. As the significance level increases from .01 to .10, does the chi-square critical value increase or decrease? Explain why.
2. As k increases from 10 to 30, does the critical value increase or decrease?
3. Explain how increasing degrees of freedom affects the critical value and the interpretation of the chi-square test statistic.

Problem Set 4.9: Identifying Parametric and Nonparametric Tests

Criterion: Distinguish between parametric and nonparametric statistical tests based on the type and scale of measurement of the data.

For each situation below, determine whether a parametric or nonparametric approach would be appropriate. Briefly explain your reasoning.

1. A researcher measures the proportion of patients with schizophrenia who were born during each season.
2. A researcher compares the average age at which schizophrenia is diagnosed among male and female patients.
3. A researcher examines whether frequency of Internet use and social interaction are statistically independent.
4. A researcher measures the amount of time, in seconds, that teenagers spend using the Internet for school-related and non-school-related activities.

Problem Set 4.10: Chi-Square Analysis Using JASP

Criterion: Conduct a chi-square goodness-of-fit analysis using JASP.

Data: Use the yummy.jasp dataset.

Tandy’s ice cream shop sells three flavors: chocolate, vanilla, and strawberry. Based on historical expectations, Tandy anticipates purchasing 100 cases of chocolate, 75 cases of vanilla, and 25 cases of strawberry, representing an expected ratio of 4:3:1.

During the current year, Tandy purchased 133 cases of chocolate, 82 cases of vanilla, and 33 cases of strawberry. The yummy.jasp dataset contains the relevant sales information.

Open the dataset in JASP and complete these steps:

1. Download and open yummy.jasp.
2. Select Frequencies from the toolbar.
3. Under Classical, select Multinomial Test.
4. Move Flavor to the Factor field.
5. Move Frequency to the Counts field.
6. Select Expected Proportions (χ²).
7. Enter the expected proportions based on the 4:3:1 ratio:
   • Chocolate = 4
   • Vanilla = 3
   • Strawberry = 1
8. Select Descriptives.
9. Select Proportions.
10. Copy and paste the JASP output into the Word document.

Then answer the following question:

Was Tandy’s observed distribution of ice cream flavors consistent with the expected distribution? Support your conclusion using the chi-square test results and significance level.

Regression

Regression analysis is used to examine relationships between variables and determine whether one variable can statistically predict another. In simple linear regression, one predictor variable is used to estimate or predict the value of a continuous outcome variable.

Problem Set 4.11: Linear Regression Analysis Using JASP

Criterion: Use JASP to determine whether age predicts life satisfaction.

Data: Use the satisfaction.jasp dataset. The dataset contains survey responses from participants of different ages who rated their life satisfaction on a scale from 1 to 10, where 1 represents very dissatisfied and 10 represents completely satisfied.

Complete the following steps:

1. Download and open satisfaction.jasp in JASP.
2. Select Regression from the toolbar.
3. Under Classical, select Linear Regression.
4. Move Life Satisfaction to the Dependent Variable field.
5. Set the analysis method to Enter.
6. Move Age to the Covariates field.
7. Under Statistics, select:
   • Descriptives
   • Estimates
   • Model Fit
8. Deselect unnecessary statistical options.
9. Copy and paste the JASP regression output into the Word document.
10. Interpret whether age significantly predicts life satisfaction based on the regression results.

Problem Set 4.12: Linear Regression Analysis Using Excel

Criterion: Conduct a linear regression analysis using Microsoft Excel.

Use the following data to examine the relationship between age and life satisfaction.

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

Complete the following steps:

1. Open a new Excel worksheet.
2. Enter X in cell A1 and Y in cell B1.
3. Enter the age and life satisfaction data in the appropriate columns.
4. Select Data Analysis from the toolbar.
5. Choose Regression.
6. Select Labels and Confidence Level.
7. Enter $B$1:$B$11 as the Input Y Range if your worksheet includes the required header and corresponding data range.
8. Enter $A$1:$A$11 as the Input X Range if your worksheet includes the required header and corresponding data range.
9. Select OK.
10. Excel will generate the regression output on a new worksheet.
11. Copy and paste the regression results into the Word document.
12. Interpret the major regression findings, including the direction and strength of the relationship and whether age significantly predicts life satisfaction.

Problem Set 4.13: Selecting Nonparametric Tests for Ordinal or Non-Normal Data

Criterion: Identify an appropriate nonparametric statistical test and explain why it is appropriate.

Read each research situation carefully. Select the most appropriate nonparametric test and briefly explain why that test is suitable for the data and research design.

Scenario 1

A researcher measures fear based on the amount of time, in seconds, participants take to walk across a portion of campus that is perceived to be frightening. The recorded times for 12 participants are:

8, 12, 15, 13, 12, 10, 6, 10, 9, 15, 50, and 52 seconds.

Identify the appropriate nonparametric test and explain why it is appropriate.

Scenario 2

Two groups of participants are given five minutes to complete a puzzle. Participants are told that the puzzle will be easy. In reality, one group receives a puzzle with a solution (Group Solution), while the other receives a puzzle with no solution (Group No Solution).

Researchers measure stress levels and find that frustration is low among participants in Group Solution, while all but a few participants in Group No Solution also have low stress levels, with several participants showing unusually high stress.

Identify the appropriate nonparametric test and explain your choice.

Scenario 3

A researcher compares student performance under three different professor conditions. In Group Adviser, the professor is also the student’s academic adviser. In Group Major, the professor teaches in the student’s major field. In Group Nonmajor, the professor does not teach in the student’s major field.

Student assignment scores are ranked within each class, and the differences in ranks are compared.

Identify the appropriate nonparametric test and explain why it is appropriate.

Scenario 4

A researcher asks the same participants to rank two different advertisements for the same product. The researchers compare the differences between participants’ rankings of the two advertisements.

Identify the appropriate nonparametric test and explain why it is appropriate.

Scenario 5

A professor measures student motivation before, during, and after a statistics course during the same semester. Student motivation is ranked at each measurement point, and the differences in ranks are compared across the three time periods.

Identify the appropriate nonparametric test and explain why it is appropriate.

Frequently Asked Questions

What is ANOVA used for?

ANOVA, or analysis of variance, is used to determine whether statistically significant differences exist between the means of two or more groups. A one-way ANOVA is appropriate when researchers examine one categorical independent variable with multiple levels and a continuous dependent variable.

What does the F statistic represent in ANOVA?

The F statistic compares variability between groups with variability within groups. A larger F statistic generally provides stronger evidence that group means differ, although statistical significance must be evaluated using the appropriate degrees of freedom and p value.

What is the difference between ANOVA and a chi-square test?

ANOVA is generally used to compare means of a continuous outcome across groups, whereas chi-square procedures are designed for categorical frequency data. A chi-square goodness-of-fit test compares observed and expected frequencies, while a chi-square test of independence examines the relationship between categorical variables.

What is a Tukey HSD test?

Tukey’s Honestly Significant Difference (HSD) test is a post hoc procedure used after a statistically significant ANOVA to determine which specific pairs of group means differ significantly.

What is a chi-square goodness-of-fit test?

A chi-square goodness-of-fit test determines whether observed categorical frequencies differ significantly from a set of expected frequencies or proportions.

What is linear regression used for?

Linear regression examines the relationship between a predictor variable and a continuous outcome variable. It can be used to determine whether changes in the predictor are associated with changes in the outcome and whether the predictor significantly contributes to explaining variation in the outcome.

What is the difference between parametric and nonparametric tests?

Parametric tests generally rely on assumptions about population distributions and are commonly used with interval- or ratio-level data that meet relevant assumptions. Nonparametric tests are useful when those assumptions are not met or when the data are ordinal, ranked, categorical, or substantially non-normal.

Why are JASP and Excel used in this assessment?

JASP provides an accessible statistical analysis environment for conducting procedures such as ANOVA, chi-square tests, post hoc comparisons, and regression. Excel also includes statistical analysis tools that can be used to perform procedures such as one-way ANOVA and linear regression.

References

Drakou, A., Tzetzis, G., & Mamassis, G. (2006). Leisure constraints experienced by university students in Greece. Sport Management International Journal, 2(1), 1–13.

JASP Team. (n.d.). JASP: A fresh way to do statistics. https://jasp-stats.org/

National Institute of Standards and Technology. (n.d.). NIST/SEMATECH e-Handbook of Statistical Methods. https://www.itl.nist.gov/div898/handbook/

OpenStax. (2023). Introductory statistics 2e. Rice University. https://openstax.org/details/books/introductory-statistics-2e

PSYC FPX 4700 Assessment 4 Anova Chi Square Tests and Regression

Penn State Eberly College of Science. (n.d.). STAT 200: Elementary statistics. https://online.stat.psu.edu/stat200/

The jamovi project. (n.d.). jamovi. https://www.jamovi.org/