PSYC FPX 4700 assessment 4 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.

As k increases (from 1 to 8), the critical values decrease. This can be seen in the F-table, where an increase in the degrees of freedom for the numerator, ????−1k−1, results in smaller critical values at both the.05 and.01 significance levels. A smaller critical value means that it is easier to be able to exceed the threshold necessary to reject the null hypothesis, holding constant the observed F-ratio as increasing with effect size and/or variance among group means. In other words, as ???? k increases, the test becomes increasingly sensitive to the detection of differences between groups.

This shows that increasing k increases the power of the test so that it can detect differences at a higher sensitivity. However, this is possible only if the sample size is large enough to accommodate the additional groups. When the number of groups is large and the sample size is fixed, then the groups become too small and power decreases.

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 – Fat Grams Consumed

Descriptives – Fat Grams Consumed

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.

3. In Row 1, enter High in cell A1, Moderate in cell B1, and Low in cell B1.
4. In the toolbar, click Data Analysis, select Anova: Single Factor, and click OK.
5. In Input Range: $A$1:$C$6, put a check next to Labels in First Row, click OK.
6. 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. On stress levels, with High, Moderate, and Low, there were no significant mean differences in terms of fat gram consumption.
2. Report your results in APA format (as you might see them reported in a journal article).

A one-way between-groups analysis of variance (ANOVA) examined the effect of level of stress (High, Moderate, Low) on fat grams consumed. Fat grams were affected by the level of stress, F(2, 12) = 4.67, p = 0.033. Students in the High stress group were reported to consume more significant amounts of fat compared to those in the Moderate and Low stress groups, results of post hoc tests.

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?

At a.05 level of significance, the significant factors are age and marital status. The results showed that there is a significant effect of age on life satisfaction, F(3, X) = 3.04, p =.029. This means that life satisfaction is different for people in different age groups. Similarly, marital status also had a significant effect, F(2, X) = 12.46, p =.000, indicating that there was a difference in life satisfaction according to marital status. On the other hand, sex, p =.409, and education, p =.536, were not significant factors because their p-values were greater than.05.

State the number of levels for each factor.

Each factor in the analysis has a number of levels. The factor sex has 2 levels: men and women. The factor age has 4 levels: people in their 20s, 30s, 40s, and 50s. Marital status has 3 levels: single, married, and divorced. Lastly, the factor education includes 4 levels: high school, postsecondary, university degree, and master’s degree. These are the categories of each factor through which differences in life satisfaction are assessed.

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 – Fat Grams Consumed

Descriptives – Fat Grams Consumed

Post Hoc Comparisons – Stress Level

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.

Significant differences were observed between the high-stress and moderate-stress groups at.05 levels of significance (p = 0.005), as well as between the high-stress and low-stress groups (p = 0.001). The difference was not significant between the moderate-stress and low-stress groups (p = 0.045).

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 column to the far left; the level of significance is listed in the top row to the right. These are the only two values you need to find the critical values for a chi-square test.

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

Increasing k and α in the chi-square table:

1. Record the critical values for a chi-square test, given the following values for k at each level of significance:

Note: Because there is only one k given, assume this is a goodness-of-fit test and compute the degrees of freedom as (k − 1).

2. As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain.

As the significance level increases from .01 to .10, the critical value decreases. This is because with a greater significance level, one can be even more liberal in making the decision to reject the null hypothesis. In other words, a smaller level of significance requires stronger evidence to reject the null hypothesis; when it is at a more stringent level (.01), the critical value is larger. Conversely, at a more lenient level (.10), less evidence is needed, so the critical value is smaller.

3. As k increases (from 10 to 30), does the critical value increase or decrease? Explain your answer as it relates to the test statistic.

As kk (degrees of freedom) increases from 10 to 30, the critical value increases. This is because the chi-square distribution becomes more spread out with higher degrees of freedom, requiring a larger test statistic to reach the same level of significance. The critical value reflects the threshold beyond which the observed data would be considered unlikely under the null hypothesis. Therefore, as kk increases, the critical value must rise to account for the greater variability in the distribution.

Problem Set 4.9: Parametric Tests

Criterion: Identify parametric tests.

Instructions: Based on the scale of measurement for the data, identify if a test is parametric or nonparametric.

1. A researcher measures the proportion of schizophrenic patients born in each season.

This is a categorical data set (seasons) with proportions, so it calls for a nonparametric test. A chi-square test for goodness-of-fit would be used to see if the proportions are significantly different from what would be expected under the null hypothesis.

2. A researcher measures the average age that schizophrenia is diagnosed among male and female patients.

This is a comparison of means based on age, a continuous variable, between two groups: male and female patients. Since the data are probably measured on an interval or ratio scale and in the assumption of normality and homogeneity of variances, the appropriate use would be a parametric test, like the independent samples t-test.

3. A researcher tests whether frequency of Internet use and social interaction are independent.

In this case, one will be testing the relationship between two categorical variables: frequency of Internet use and social interaction. An appropriate test in this scenario would be a nonparametric test, such as the chi-square test for independence, to establish if there is any significant association between these variables.

4. 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.

Compare, in this scenario, the quantity of time, a continuous variable, spent on two related activities: school-related and non-school-related Internet use. Since data are likely to be measured at an interval or ratio scale and assuming normality, a parametric test-the paired samples t-test-would apply.

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 the future years. She knows that on average she 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 is a record of ice cream sales 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. In the menu that appears, under Classical, select Multinomial Test.
3. Select Flavor and then click the upper Arrow to send it over to the Factor box.
4. Select Frequency and then click the lower Arrow to send it over to the Counts box.
5. Click the circle next to Expected Proportions (χ²).
6. Fill in 4 for Chocolate, 1 for strawberry, and 3 for Vanilla.
7. Select the box for Descriptives and click the circle next to Proportions.
8. Copy and paste the output to the Word document.
9. Answer this: Was Tandy’s distribution of proportions the same as expected?

Multinomial Test

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 is a record of responses to a survey which asked participants of various ages to rate their level of life satisfaction on a 1–10 scale, with 1 being “very dissatisfied” and 10 being “completely satisfied”:

Instruction: Complete steps below.

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

Model Summary – Life Satisfaction

Problem Set 4.12: Analysis of Regression in Excel

Criterion: Use Excel to complete an analysis of regression.

Data: Use the data from this table

Instructions: Complete the following steps.

1. Open Excel and work in a new sheet.
2. Enter the data from the table in Problem Set 4.11. Cell A1 will be X. Cell B1 will be Y. Then, enter the data below.
3. Go to the tool bar, click Data Analysis, and select Regression.
4. Put a check next to Labels and Confidence Level.
5. In Input Y Range: $B$1:$B$11, In Input X Range: $A$1:$A$11
6. Select Ok. Your data will appear in a new Sheet to the left.
7. Copy and paste the output to 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.

1. 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.

The appropriate nonparametric test for this data is the Wilcoxon Signed-Rank Test because the data is paired and not normally distributed.

2. Two groups of participants were given 5 minutes to complete a puzzle. The participants were told that the puzzle would be easy. In truth, in one group, the puzzle had a solution (Group Solution), and in the second group, the puzzle 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 showed strikingly high levels of stress in Group No Solution.

The appropriate nonparametric test for these data will be the Mann-Whitney U Test, as it is applied to compare two independent groups with skewed distributions.

3. 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; 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 appropriate for this kind of data since it is used in the comparison of more than two independent groups using ranked data. The test is suitable when assumptions of normality for ANOVA are not met.

4. A researcher has the same participants rank two types of advertisements for the same product. Differences in ranks for each advertisement were compared.

This nonparametric test for the above data is Wilcoxon Signed-Rank Test since it contrasts matched rankings by the same subject for two conditions related to each other. The test is ideal for ordinal data or when normality is assumed not to be satisfied.

5. 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.

The appropriate nonparametric test for such data is the Friedman Test because it compares ranks across three or more related conditions, namely before, during, and after taking the course by the same subjects. Such a test is again suitable for ordinal data or repeated measures.