Interpretation of Independent t-Tests and ANOVA
Suppose that we are interested in comparing dietary sodium intake (NA) between men and women. We analyze the data using SAS's TTEST procedure and observe the results shown in Table 1 (see page 6). Based on those findings, answer the following questions. PLEASE SHOW HOW YOU GOT THE ANSWER.
1) Report and interpret the 95% confidence interval of the dietary sodium intake for men. [Report two decimal places]
2) Identify the dependent variable and the independent or explanatory variable(s) in this study. Also, state the Null and Alternative hypotheses.
Dependent Variable: ________________
Independent Variable: ________________
Null Hypothesis:
Alternative Hypothesis: ________
3) An important step in an Independent t-Test is to first test for equal variances. Based on the information in the "Equality of Variances" portion of the output table, what is your decision about the Null hypothesis regarding equal variances (i.e. H0: Variance1 = Variance2)? In your answer, report the test statistic and P-value from the SAS output that you used to make your decision.
4) Now we want to test the Null hypothesis that was stated in Question 2. From the "T-Tests" portion of the output, report the test statistic and P-value that should be used to test the Null hypothesis. Based on that information, what conclusion can you make about the Null hypothesis (i.e. Reject or Fail to Reject the Null)?
5) Interpret these findings (3-4 sentences max). Your answer should (1) restate the findings, (2) note the generalizability of these results, and (3) state what these findings mean from clinical perspective.
PART TWO: ANOVA
Suppose that we are interested in examining diastolic blood pressure (DBP) by gender and three hypertension medications. We recruit 120 hypertensive patients and randomly assign them to one of six study groups - 20 individuals in each group.
In our analysis, we create a variable called "GEN_DRUG" to reflect the six possible group combinations of gender and medication. The variable is coded as follows:
After one year, we measure the DBP (mmHg) of all participants. We are interested in comparing mean DBP across the six study groups. We analyze the data using SAS's ANOVA procedure and observe the results shown in Table 2 (see page 7). Based on those findings, answer the following questions.
1) Identify the dependent variable and the independent or explanatory variable(s) in this study. Also, state the Omnibus (or Overall) Null and Alternative hypotheses.
Dependent Variable: ________________
Independent Variable: ________________
Omnibus Null Hypothesis:
Omnibus Alternative Hypothesis:
2) If this null hypothesis is true, then we would expect to see that the average variation between the means (i.e., the "model mean square" in SAS) is equal to the average variation within each group (i.e., the "error mean square" in SAS). We compare the two mean squares as an F ratio, dividing the model mean square by the error mean square.
Locate the two mean squares on the SAS output table and calculate the F ratio. Show your work.
3) Report the test statistic and P-value from the SAS output. Based on that information, what conclusion can you make about the Omnibus (or Overall) Null hypothesis (i.e. Reject or Fail to Reject the Null)?
4) Based on the information from the Student-Newman-Keuls post hoc test, make a bulleted list of what GEN_DRUG groups are significantly different from each other and what groups are not. [Be sure your answer is thorough.]
5) Interpret these findings (3-4 sentences max). Your answer should (1) restate the findings, (2) note the generalizability of these results, and (3) state what these findings mean from clinical perspective.