Using SPSS To Run Some Advanced Statistical Analyses: MANOVA and MANCOVA.

CASE STUDY: MANOVA

This case requires that you present a research question and hypothesis, test it, and run a series of SPSS statistical tests to support your findings. The only mandatory statistical test that you have to perform is a MANOVA/MANCOVA.

Noise Testing in Classrooms

For the Noise-Testing Scores v4 SPSS data base you are to do the following tasks:

1. Present a Research Question and hypothesis.

2. Perform the appropriate statistical analyses to answer your hypothesis and research question.

· Be sure to perform the various statistical tests which are needed to support your findings for your original research question and allow you better interpret the results of your ANOVAs and MANOVAs. You can also run Chi-Square or correlations, descriptives, and t-Tests

3. Interpret all test results and report all statistic.

4. State your conclusions

Solution: The research hypothesis is whether Ethnicity and Household Income affect both the Reading Test Score and the Math Test Score.

For this purpose, a MANOVA analysis will be used. The descriptive statistics of the quantitative variables are shown below:

Now, for the categorical variables we get

Now, the results of running a MANOVA with SPSS are shown:

The homogeneity assumptions are basically satisfied, except for the homogeneity of variances for Math test score (p = 0.042).

The main multivariate table is shown below:

Surprisingly enough, none of the variables is significant (all the p-values are greater than 0.05).

Hence, we reject our research hypothesis: We conclude that whether Ethnicity and Household Income don’t affect the Reading Test Score and the Math Test Score.

Ugandan Database

Repeat the same set of questions above for the Ugandan database. Ugandan dataset

For both datasets please be sure to only present results which are useful and have value (utility).

Solution: The research hypothesis is that age of first marriage and age at first sexual intercourse are affected by the variable Type of place of residence and Watches to TV every week.

In order to test for our research hypothesis, we need to run an MANOVA, with age of first marriage and age at first sexual intercourse as the response variable and Type of place of residence and Watches to TV every week as predictors.

We have the following descriptive statistics of the quantitative variables:

For the qualitative variables we have

The following are the results of the MANOVA analysis obtained with SPSS:

· First we have a descriptive analysis:

The homogeneity assumptions are met, except for the case of homogeneity of variances for Age at the first sexual intercourse (p = 0.041).

· Below we have the main multivariate table:

The table above shows that Type of place of residence is significant (p = 0.012), whereas Watches TV every week is not (p = 0.450). Also, the interaction term is not significant as well (p = 0.319).

Means Plot

As we can see, for both response variables, the mean is significantly lower for rural group than for the urban group.

Part Two: Health Scare

The World Health Organization recently announced that the virus causing HBPS (Hemorrhagic Black Pox Syndrome) in Athens, Greece is a new pathogen that has never been seen before in humans.

Within 24 hours after arriving in Athens, you developed a standardized questionnaire to determine the likely source of the outbreak. Within a couple of days, you interviewed 45 cases and 35 controls about their clinical symptoms and exposures. During your interviews, you have discovered that a number of individuals just returned home about six weeks ago from a 1-month military mission abroad in Kinshasa, Zaire. Based on preliminary analysis of your data, it appears that either travel history to Zaire and/or residing near the airport may be associated with HBPS.

What type of study design are you using to investigate the source of transmission? Explain.

What surveillance methods would you use to find additional cases?

What is your hypothesis?

How would you select controls for this investigation? Would you use matching? Why or why not?

Analyze the exposure data below by calculating the appropriate measure of association and 95% confidence intervals for each exposure among the cases and unmatched controls. Use stratification to separate the confounding effects of the other exposure. Show your work in the calculating the measures of association. For the 95% confidence intervals, you may find one of the confidence interval calculators above useful.

What does your analysis suggest regarding the likely source of exposure? What further studies would you suggest to investigate the outbreak

Solution: Here we have a Case-control study in order to determine whether the odds of having the condition is higher for those who traveled to Kinshasa (retrospective study), and also we have Cohort Study, required to analyze the incidence in the risk of acquiring the disease for people living near the airport compared to people who live farther away from the airport.

• Odds Ratio

We have the following table:

We compute the odds ratio and the 95% confidence interval. The results are shown below:

The odds ratio is therefore OR = 3.89, and the 95% confidence interval is (1.414, 10.726), which means that the odds ratio is significantly greater than 1. In other words, having traveled to Kinshasa significantly increases the odds of having HBPS.

• Relative Risk

We have the following table:

We compute the relative risk and the 95% confidence interval. The results are shown below:

The relative risk is therefore RR = 2.797, and the 95% confidence interval is (1.664, 4.70), which means that the relative risk is significantly greater than 1. In other words, living nearby the airport significantly increases the risk of contracting HBPS.

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