Given Hapunda

150 Inferential Statistics in Data Analysis Inferential statistics allow the evaluator to make inferences about the population from which the sample data were drawn based on probabilities. Inferential statistics are grounded in the concept of probability, or the likelihood of an event occurring. They rely on statistical significance, or a way of giving odds for or against the probability that something happened strictly by chance. Testing for statistical significance helps ensure that differences observed in data, however small or large, were not due to chance. For example, suppose descriptive statistics found that the proportion of children who were vaccinated for the Rubella Virus in February 2018 did not have side effects like diarrhoea and fever caused by the vaccine and that these side effects occurred only by chance compared to those who were in the control group. Here, you could ask a question of whether the vaccine caused the diarrhoea and the fever. Whether the difference between those vaccinated and those in the control (NOT vaccinated) differ significantly to conclude that the vaccine caused the diarrhoea and the fever. To answer this question, you could conduct a statistical test to tell you how likely it would be to observe a difference of this size by random chance alone. Suppose that the statistical test indicated that this difference was significant at the 95% confidence interval. This would mean that the likelihood of this difference being due to random chance is only 5% out of 100%. Thus, you could conclude with a high degree of confidence that the vaccine caused the diarrhoea and fever. A few statistical tests have been covered in this chapter to aid exploring and conducting such tests in SPSS. It is advisable to purchase a statistics textbook that will provide the information needed to conduct such and other statistical tests. Tests of Difference for two Sample Designs - T-tests The t- test is a test that is used to determine whether two group means are significantly different from one another. T -tests are parametric tests that make certain assumptions about the data. The assumptions include; a) The data is measured on either an interval or ratio scale. b) There is homogeneity of variance. c) The population from which the data is drawn has a normal distribution. There are basically three types of t -tests.  Single sample t-test - this is the simplest t -test and determines whether the observed mean is different from a set value. This set value is the benchmark that determines the difference in the mean.