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: .05 .01 k = 2 k = 4 k = 6 k = 8 ___ ___ ___ ___ ___ ___ ___ ___ 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 SPSS Criterion: Calculate an ANOVA in SPSS. Data: The following is the amount of fat (in grams) consumed in a buffet-style lunch among professional bodybuilders under conditions of high, moderate, and low stress: Stress Levels High Moderate Low 10 9 9 7 4 4 8 7 6 12 6 5 6 8 7 Instructions: Complete the following steps: a. Open SPSS and open a New DataSet. b. Click the Variable View tab at the bottom and enter Stress and enter Fat as the variables. Click the Values box for the Stress row and define 1 as high, 2 as medium, and 3 as low. c. Enter the data. For example, type 1 in row 1 under Stress and type 10 in row 1 under Fat. Continue typing in all the data. Please remember to change to 2 in column 1 when the stress is moderate and change to 3 in column 1 when the stress is low d. In the Toolbar, click Analyze, select Compare Means, and then select One-Way ANOVA. e. Select Fat and then click Arrow to send it over to the Dependent List box. f. Select Stress and then click Arrow to send it over to the Factor box. g. Click OK and 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 Problem Set 4.3 to complete the following steps: a. Open Excel to an empty sheet. b. Enter the data from Problem Set 4.3. c. In Row 1, enter High in cell A1, Moderate in cell B1, and Low in cell B1. d. In the toolbar, click Data Analysis, select Anova: Single Factor, and click OK. e. In Input Range: $A$1:$C$6, put a check next to Labels in First Row, click OK. f. 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: a. State the null hypothesis. ___________________________________ b. 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, Kambitsis, Charachousou, and Tzetzis (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. 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 1. Which factors were significant at a .05 level of significance? _____________________ State the number of levels for each factor. ____________________________________ Problem Set 4.6: Tukey HSD Test in SPSS Criterion: Calculate post hoc analyses in SPSS. Data: Use SPSS data from Problem Set 4.3. Instructions: Complete the following steps: a. In the Toolbar, click Analyze, select Compare Means, and then select One-Way ANOVA. b. Select Fat then click Arrow to send it over to the Dependent List box. c. Select Stress, then click Arrow to send it over to the Factor box. d. Click Post Hoc and then check the box Tukey. Click Continue. e. Click OK and copy and paste the output to the Word document. Problem Set 4.7: Tukey HSD Interpretation Criterion: Interpret Tukey HSD results from SPSS 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 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 a 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: .10 .05 .01 k = 10 ___ ___ ___ k = 16 ___ ___ ___ k = 22 ___ ___ ___ k = 30 ___ ___ ___ 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. ___________________________________ 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. ___________________________________ 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. A researcher measures the proportion of schizophrenic patients born in each season. ___________________________________ A researcher measures the average age that schizophrenia is diagnosed among male and female patients. ___________________________________ A researcher tests whether 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 SPSS Criterion: Use SPSS for a chi-square analysis. Data: 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, the ice cream sales increased, and she purchased 133 cases of chocolate, 82 cases of vanilla, and 33 cases of strawberry. Instructions: Complete the following steps: a. Open SPSS and create a New DataSet. b. Go to the Variable View tab and type Flavor in the first row and Frequency in the second row. Adjust the decimal value to 0. Go to Values in the Flavor row and enter 1 for chocolate, 2 for vanilla, and 3 for strawberry and click OK. c. Go to the Data View tab and under the Flavor column, enter 1 in row 1, 2 in row 2, and 3 in row 3. Under the frequency column, enter 133 in row 1, 82 in row 2, and 33 in row 3. d. In the Toolbar, click Data, then select Weight Cases. e. Select Weight Cases By, select Frequency, and then click Arrow to send it over to the Frequency Variable box. Click OK. f. In the Toolbar, click Analyze, then Nonparametric Tests, then Legacy Dialogs, and then Chi-Square. g. Select Flavor and then click Arrow to send to the Test Variable List. h. Under Expected Values, select Values and then enter the following three values in the order: 100, 75, and 25. i. Click OK and copy and paste the output to the Word document. j. Answer this: Was Tandy’s distribution of proportions the same as expected? Regression Problem Set 4.11: Analysis of Regression in SPSS Criterion: Use SPSS to complete an analysis of regression. Data: 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: Complete the following steps. a. Open SPSS and create a New DataSet. b. Go to the Variable View tab and type X in the name column, then enter Y in the column below it. c. Go to Data View and enter the data from the table above. d. Go to the tool bar, click Analyze, select Regression, then select Linear. e. Select Y and then click the Arrow to send to Dependent. f. Select X and the click the Arrow to send it to Independent(s). g. Select Ok. Copy and paste the output to 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 Problem Set 4.11. Instructions: Complete the following steps. a. Open Excel and work in a new sheet. b. 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. c. Go to the tool bar, click Data Analysis, and select Regression. d. Put a check next to Labels and Confidence Level. e. In Input Y Range: $B$1:$B$11, In Input X Range: $A$1:$A$11 f. Select Ok. Your data will appear in a new Sheet to the left. g. 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. ___________________________________ 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. ___________________________________ 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. ___________________________________ 4. A researcher has the same participants rank two types of advertisements for the same product. Differences in ranks for each advertisement were compared. ___________________________________ 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 co
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