The t-tests and analysis of variance (ANOVA) tests are perhaps the most famous statistical tests. However these tests rely very heavily on the fulfillment of key assumptions by the data under investigation. Some of these assumptions (such as normality and homogeneity of variance) are not always realized by most real world data, and as a consequence transformation of data and/or an application of alternative statistical methods may be needed in some cases. Therefore, checking these assumptions is a crucial task to be addressed by the researchers. Violations in underlying assumptions can lead to erroneous conclusions.
The purpose of this course is to review basic motivation for and assumptions underlying t-tests and ANOVA, and also to describe alternative non parametric (i.e. rank based) tests. This course covers t-tests and ANOVA including the one sample t-test, Independent Samples t–test, paired t-tests, One way ANOVA test, and the repeated measurement one way ANOVA test. An alternative rank based test (i.e. The Wilcoxon signed Rank Test, The Mann Whitney Test, Kruskali Wallis Test, and Friedman Test) will be introduced in each case.
The course uses real data taken from post graduate students' works at Sokoine University of Agriculture (SUA) in Tanzania-East Africa and the SPSS software, which is user-friendly. The data pertains to different research problems encountered by the postgraduate students. One data set looks at rural women's income poverty based on a sample of 30 women whereas another data set examines chickens' performance based on a sample of 16 chickens. Another data set compares length of stay between tourists on package tour against those on non-package tour based on two different samples of 36 tourists each. In another case, a data set compares profit margins among 85 tomato business actors at different nodes of tomato value chain and the aim is to find out which type of actors earns the highest profit margin. Another data set compares secondary school students’ examinations results in three different localities (Rural, Semi Rural and Urban) given in letter grades. Another data set compares performance of 20 randomly selected students in three different English tests whereas the last data set compares performance of 162 students across 4 different semesters of study based on their GPAs.