Factorial Analysis Of Variance And Hypothesis Testing In Relation To Professional Athletes’ Healthy Eating Habits

Factorial Analysis of Variance in Relation to Professional Athletes’ Healthy Eating Habits

A sports psychologist gave a questionnaire about healthy eating habits to randomly selected professional athletes. The results are displayed below. Using the .05 significance level, is there a difference in healthy eating habits among professionals in the three sports?

Baseball Players              Basketball Players              Football Players

            32                                    27                                        27

            27                                    36                                        23

            26                                    25                                        26

            35                                    30                                        20

1. Make a graph for the data set.

Answer 

Use the five steps of hypothesis testing (report results in APA format).

Step1: Null and Alternative hypothesis

At 5% level of significance

Step 2: Test Statistics

To test the hypothesis analysis of variance (ANOVA) test will be performed.

Step 3: Critical value

We find the critical value at 5% level

Step 4: Decision

The null hypothesis is rejected if the computed F value is greater than the F-critical value otherwise the null hypothesis is accepted.

Step 5: Conclusion

The computed F-value (0.0156) is less than the F-critical (4.2565) hence the null hypothesis is not rejected as such we conclude that there is no significant difference in healthy eating habits among professionals in the three sports.

Effect size output

The overall effect size f = 0.0510
The effect size for Group 1 vs Group 2 is f = 0.0442
The effect size for Group 1 vs Group 3 is f = 0.0442
The effect size for Group 2 vs Group 3 is f = 0.0000

1. Conduct a planned contrast for Baseball versus Football players (using Tukey’s HSD).

Answer

Results of the post-hoc Tukey HSD showed that there is no significant difference in healthy eating habits between the Baseball and football players.

1. (25 points) A researcher is interested in the effects of sleep deprivation and caffeine intake on mood. Participants were randomly assigned to a sleep condition (normal or deprived) and a caffeine condition (0 cups, 2 cups, or 4 cups). After the manipulations, mood was measured (such that higher numbers indicated better mood). The results were as follows:

               Normal Condition                            Deprived Condition

            0 cups  2 cups  4 cups                          0 cups  2 cups  4 cups

                16       18         18                                0          5          6

                17       20         17                                6          4          8

                20       20         17                                3          4          6

                19       19         17                                2          2          7

                18       18         16                                4          5          8

Analyze these data using a factorial analysis of variance and including R² for each effect.

Answer

Results shows that there was a statistically significant two-way interaction between Caffeine and Sleep, F(2, 24) = 10.87, p = .000.

The value of R-Squared is 0.968; this implies that the two factors (caffeine and sleep conditions) together with their interaction explain 96.8% of the variation in the mood score.

1. (25 points) A researcher was interested in whether college GPA (X) would predict starting salary after college (Y). (For simplicity, salary was converted to a 100-point scale.) The participants’ scores were:

            X                      Y         

            2.25                 55

            1.75                 23

            3.25                 80

            3.75                 42       

            M = 2.75          M = 50 

1. Report the correlation and linear prediction equation.

Answer

Correlation

The correlation coefficient between x and y is 0.4807; this implies a weak positive correlation between the two variables (X and Y).

Linear prediction equation;

1. Make a graph with the regression line.

Answer

The standardized regression coefficient is 0.481.

1. (25 points) An advertising firm wanting to target people with strong desires for success conducted a study to see if such people differed in the types of television shows they watched. Randomly selected participants recorded the shows they watched for a week, then their desire for success was assessed, and finally they were divided into two groups. Low Success seekers watched 8 comedies, 15 romances, 6 documentaries, 13 dramas, and 3 news shows. High Success seekers watched 3 comedies, 3 romances, 9 documentaries, 7 dramas, and 8 news shows. Using the .05 significance level, is the distribution of type of shows watched different for participants having high and low desires for success?

Use the five steps of hypothesis testing.

Answer

Step1: Null and Alternative hypothesis

H₀: There is no significant association between desire for success and type of television shows watched

H_A: There is significant association between desire for success and type of television shows watched

At 5% level of significance

Step 2: Test Statistics

To test the hypothesis Chi-Square test of association will be performed.

The chi-square statistic is 12.4432. The p-value is .014343.

Step 3: Critical value

We find the critical value at 5% level

Step 4: Decision

The null hypothesis is rejected if the computed Chi-Square value is greater than the critical Chi-Square value otherwise the null hypothesis is accepted.

Step 5: Conclusion

The computed Chi-Square value (12.4432) is greater than the critical Chi-Square value (9.4877) hence the null hypothesis is rejected as such we conclude that there is significant association between desire for success and type of television shows watched.

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