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158 The above output shows the bivariate associations between the variables under investigation. These Bivariate analyses reveal that there is a strong positive correlation between the number of people in the house and malaria case reported as, r = .834 (140), p < .001. Analysis of Variance The purpose of Analysis of Variance (ANOVA) is much the same as the t -tests but the goal is to determine whether the mean differences that are obtained for sample data are sufficiently large to justify a conclusion that there are group mean differences between the populations from which the samples were obtained. These procedures produce an analysis for a quantitative dependent variable affected by a single factor (independent variable). Analysis of variance is used to test the hypothesis that several group means are equal. This technique is an extension of the two-sample t- test. The difference between ANOVA and the t -tests is that ANOVA can be used in situations where there are two or more group means being compared. Whereas the t- tests are limited to situations where only two means are involved. Analysis of variance is necessary to protect researchers from excessive risk of a Type I error where multiple comparisons produce inflated group mean differences that reject the null hypothesis when it is actually true in situations where a study is comparing more than two population means. These situations would require a series of several t tests to evaluate all of the mean differences. (Remember, a t -test can compare only 2 means at a time). Although each t test can be done with a specific α -level (risk of Type I error), the α -levels accumulate over a series of tests so that the final experiment wise α -level can be quite large. ANOVA allows researchers to evaluate all of the group mean differences in a single hypothesis test using a single α -level, thereby, keeping the risk of a Type I error under control no matter howmany different group means are being compared. ANOVA Assumptions Like other techniques, the ANOVA also has to fulfill certain assumptions before it can be calculated. a) The dependent variable comprises data measured at interval or ratio scale b) Data is drawn from the population is normally distributed c) There is homogeneity of the variance, that is, the samples being compared are drawn from the populations which have the same variance A typical situation to use the ANOVA is when three separate samples are obtained to evaluate the mean differences among three populations (or treatments) with unknown means. Thus: