Bivariate Analysis T-TEST. Comparison of means: t-test. Outline. Hypothesis testing steps. Comparison of means: t-test

Transcription

1 Bivariate Analysis T-TEST Variable 1 2 LEVELS >2 LEVELS CONTINUOUS Variable 2 2 LEVELS X 2 >2 LEVELS X 2 CONTINUOUS t-test X 2 X 2 ANOVA (-test) t-test ANOVA (-test) -Correlation -Simple linear Regression Outline Hypothesis testing steps T-test Anova T-test is used when one variable is of a continuous nature and the other is dichotomous. The t-test is used to compare the means of two groups on a given variable. Examples: in average blood pressure among s & fes. in average BMI among those who exercise and those who do not. Hypothesis testing steps Identify the study objective State the null & alternative hypothesis Select the proper test statistic Calculate the test statistic Take a statistical decision based on the p-value. Reject or accept the null hypothesis Example 1: Research question: Among university students, is there a difference between the average for s versus fes? Null hypothesis (H o ): μ s = μ fes Alternative hypothesis (H a ): μ s μ fes Statistical test: t-test

2 T-Test (SPSS output) fe If this p-value is < 0.05 then reject null hypothesis and conclude that the variances are different (accept alternative) and hence check this p-value for the t-test. If this p-value is > 0.05 then accept null hypothesis and conclude that the variances are equal and hence check this p-value for the t-test. Mean Mean This is the p-value for the t-test (of whether the mean of for s = mean of for fes -- in the population). Need to chose either the upper or the lower value to conclude whether there is a significant difference in between 2 groups. The choice is done based on the test of whether variances of the 2 groups are equal or not. Mean Example 1: Research question: Among university students, is there a difference between the average for s versus fes? μ s = μ fes μ s μ fes Statistical test: t-test t-test= P=0.000 Conclusion: At significance level of 0.05, we reject null hypothesis and conclude that in the population there is a significant difference in the average of s & fes. This is the p-value that tests whether the variances are equal or not. H o : variance of s = variance of fes H a : variance of s variance of fes Mean Mean

3 average for versus students? Mean Conclusion: At significance level of 0.05, we accept the null hypothesis and conclude that in the population there is no significant difference in the average of and students. fe μ = μ μ μ Mean Mean fe average for s versus fes? 0.189

4 fe μ s = μ fes μ s μ fes Mean Mean average for versus students? Mean Conclusion: At significance level of 0.05, we reject the null hypothesis and conclude that in the population there is a significant difference in the average of s and fes. μ = μ μ μ

5 Mean SPSS commands for t-test Example 3 select as the dependent variable select as the independent variable Example 4 select as the dependent variable select as the independent variable Mean END Conclusion: At significance level of 0.05, we accept the null hypothesis and conclude that in the population there is no significant difference in the average of and students. SPSS commands for t-test Example 1 select as the dependent variable select as the independent variable Example 2 select as the dependent variable select as the independent variable