W7_Hendrickson_Assignment

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Statistics

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Jan 9, 2024

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u07a1 – ANOVA 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.) Submit the document to your instructor by Sunday, 11:59 p.m. central time. Problem Set 7.1: Critical Value Criterion: Explain the relationship between k and power based on calculated k values. Instructions: Read the following and answer the question. 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 ): 1. 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 2-1=1; 4.30 4-1=3; 3.10 6-1=5; 2.77 8-1=7; 2.66 24-2=22; 7.95 24-4=20; 4.94 24-6=18; 4.25 24-8=16; 4.03 2. 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, the critical value decreases. As k increases, the power increases. Problem Set 7.2: Interpret ANOVA Results Criterion: Interpret the results of an ANOVA. Instruction: 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
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? Age and marital status were significant at a .05 level of significance. 2. State the number of levels for each factor. Sex: 2 levels, Age: 4 levels, Marital Status: 3 levels, Education: 4 levels. Problem Set 7.3: One-way ANOVA in JASP Criterion: Calculate an ANOVA in JASP. Data: Use the Stress data set. This data set 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 data set. Double-click the icon to open the data set 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 2
ANOVA - Fat Grams Consumed Cases Sum of Squares df Mean Square F p Stress Level 15.600 2 7.800 1.773 0.212 Residuals 52.800 12 4.400 Note. Type III Sum of Squares Descriptives Descriptives - Fat Grams Consumed Stress Level N Mean SD SE Coefficient of variation High 5 8.600 2.408 1.077 0.280 Low 5 6.200 1.924 0.860 0.310 Moderate 5 6.800 1.924 0.860 0.283 Problem Set 7.4: One-way ANOVA in Excel Criterion: Calculate an ANOVA in Excel. Instructions: Use the data from the table below to complete the following steps: a. Open Excel to an empty sheet. b. Enter the data from this table: Stress Levels High Moderate Low 10 9 9 7 4 4 8 7 6 12 6 5 6 8 7 c. In Row 1 , enter High in cell A1, Moderate in cell B1, and Low in cell C1. 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. Anova: Single Factor 3
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SUMMARY Groups Count Sum Average Variance High 5 43 8.6 5.8 Moderate 5 34 6.8 3.7 Low 5 31 6.2 3.7 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 15.6 2 7.8 1.772727 0.211576 3.885294 Within Groups 52.8 12 4.4 Total 68.4 14 Problem Set 7.5: One-way ANOVA Results in APA Style Criterion: Report ANOVA results in APA format. Data: Use the results from Problem Set 7.4. Instructions: Complete the following: a. State the null hypothesis. The null hypothesis is that there is no difference in the stress levels . . Report your results in APA format (as you might see them reported in a journal article). A one-way ANOVA examined the relationship between fat consumption and stress levels. The following one-way ANOVA results show an insignificant relationship between fat consumption and stress levels F(2,12) = 1.773, p=.212. Problem Set 7.6: Tukey HSD Test in JASP Criterion: Calculate post hoc analyses in JASP. Data: Use Stress data set from Problem Set 7.3. Instructions: Complete the steps below. (Note: The first 7 steps below are repeated from Problem Set 7.3.). 1. Download Stress data set. Double-click the icon to open the data set 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. 4
Post Hoc Tests Standard Post Hoc Comparisons - Stress Level Mean Difference SE t p tukey Hig h Low 2.400 1.327 1.809 0.208 Moderat e 1.800 1.327 1.357 0.393 Low Moderat e -0.600 1.327 -0.452 0.894 Note. P-value adjusted for comparing a family of 3 Problem Set 7.7: Tukey HSD Interpretation Criterion: Interpret Tukey HSD results from JASP output. Data: Use your output from Problem Set 7.6. Instructions: Identify where significant differences exist at the .05 level between the stress levels. There are no significant differences that exist. Problem Set 7.8 Variables for Week 9 Assignment Criterion: Define your two variables for the Week 9 Assignment. Instructions: In this section you need to define the two specific variables you selected from the Grades data file for use in the Week 9 assignment and you need to define them in the following ways: (1) variable name and definition, (2) scale of measurement (nominal, ordinal, interval, or ratio) which ties into WHICH type of statistical analysis you can use (Privitera, 2018). Variable 1: Extra Credit (DV) Variable 2: Year (IV) Variable Definition Completing extra credit opportunities The amount of years the participant has been in high school (Freshman-1, sophomore- 2, junior-3, or senior-4) Scale of Measurement Nominal Scale Ordinal Scale Statistical Analysis that should be used: Difference of proportion (z score) Reference Privitera, G. J. (2018). Statistics for the behavioral sciences (3rd ed.). Sage. 5