ANOVA Applications: Exploring Statistics for Various Studies

#1 . Which type of ANOVA would you use for each of the studies below? 1. Measure the self-esteem of the same group of college students at the beginning, middle and end of their freshman year. - One-way within subject (repeated measures) – the same group of college students is repeated measured at each level (beginning, middle, and end). The variance of this one population is not known. 2. Compare math skills for three different professional groups: physicians, attorneys and psychologists. - One-way between subject (independent groups) – different professional groups are observed on one factor (math). The variance of this one population is not known. 3. Measure Body Mass Index (BMI) for persons who take Supplement X vs. a placebo and who either exercise regularly or don’t. So there are four groups: 1) Exercise/Take Supplement X, 2) Don’t Exercise/Take Supplement X, 3) Exercise/Take Placebo, 4) Don’t Exercise/Take Placebo - Two-way between subject – Here multiple groups are put together with different participants with the combination of two different factors. 4. Look at satisfaction with mental health services based on the client’s ethnicity (White, Black, Hispanic, Asian or Other) and how they were greeted on their initial visit (receptionist smiles or does not smile). - Two-way between subject – Similar to question three, different participants in each group are observed while combining two different factors. #2. Perform a one-way ANOVA to look at whether income (INC1) differs by type of relationship (RELAT). Which of the following describes your result: D. F (3,396) = 6.85, p < .001

A one-way ANOVA was completed and based on the results we can determine that there is a significant difference between income (INC1) and different types of relationships (RELAT). In this case I would reject the null hypothesis. To reach this conclusion the following steps were taken. The Critical Value (CV) was determined by utilizing the F table at alpha 0.01 for F(df1,df2). With utilizing our data F(3,396) with a CV of 3.78. We then use the sum of squares in group one, divided by the degrees of freedom in group on to get the mean square between groups. Repeat this process with the within group data to get the mean square error. Then divide the mean square between group by the mean square error, which will give us the mean square for the test statistic, with our data set you will see that F=6.85. We can now compare the obtained value ( 6.86) by the critical value (3.78). This signifies that the obtained value is greater than the CV and there for falls in the rejection region, which supports the decision to reject the null hypothesis. Another supporting factor would be the P-value, based off of our date we can see that our p-value is less than .001, which is statistically significant, again supporting the rejection of the null hypothesis. #3. The main effect due to gender indicates that: B. Men earn more than women.

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First, the SPSS output labeled Descriptive Statistics shows the mean income of men ($62,389) and the mean income of women ($31,836.44). We can see that the mean income of men is larger than women. Second, the SPSS output of Test of Between-Subject Effects, you will see that the sig. of a 2-tailed test or p-value for GENDER1 variable is 0.000. We utilize the sig. to determine if the test is statistically significant. When considering our data set, we can see that our p-value (0.000) is less than alpha .05. This result tells us that the result is significant and there is a main effect. Last, the SPSS output labeled Estimated Marginal Mean of Income shows us that Men, which are blue in the bar graph have a larger income then women when they are single and when they are married. While the graph shows a possible main effect or interaction, we must use the test statistic to determine if a main effect or interaction is significant. Based on these three reasons we can determine that men earn more than women. #4. The main effect due to marital status indicates:

D. Married people tend to earn more than single people.

First, the SPSS output labeled Descriptive Statistics we can see the total mean of single participants is $36,306.48 and the total mean of married participants is $54,545.20. We can see that married participants make significantly more than single participants. Second, SPSS output labeled Test of Between-Subjects Effects shows that the sig. or p-value of a 2-tailed of MSTAT is . 000, which is less than alpha .05. Because . 000 is less than .05, we can determine that the test is significant and there is a main effect. Lastly, similar to the SPSS output Descriptive Statistics the Estimated Marginal Means Income shows that married individuals make more than single individuals. The red line represents married individuals, which is above the blue line which is single individuals. #5. The interaction effect indicates: B. The male/female income difference is greater when comparing married people than when comparing singles.

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When considering our data set, the interaction data set is referring to the interaction effect of income in relation to gender (male/female) and marital status (married/single). Let’s now look at the sig of a 2-tailed for GENDER1*MSTAT, which reads .025. GENDER1*MSTAT is the interaction effect variable. This variable is less than .05 which tells us that there is a significant interaction effect. In addition, when you look at the Estimated Marginal Mean of Incomes you will see the difference between the red line of married individual is higher and does not intersect the blue line of single individual, which is lower.

Because the lines do not touch, we are able to determine that there is an interaction effect.

Activity 10- Statistics Exercise IV

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