Some Statistical Tests

Paired Sample T Test

• The Paired Samples T Test procedure compares the means of two variables for a single group. It computes the differences between values of the two variables for each case and tests whether the average differs from 0.
• For administering Paired Samples T Test both the variables should be normally distributed. We can check for normal distribution with Q-Q Plot from Graph menu of the SPSS window.
• The SPSS shows a number of results such as descriptive statistics including mean, satandard deviation and the pair; correlation between the variables including the significance value; and the result of the T Test.
• The Paired Samples T Test is based on the difference between the two variables. Under 'Paired Differences' we see the descriptive statistics for the difference between the two variables.
• To the right of the paired difference we see the T, degrees of freedom, and significance.
• If the T value is 0.601, the degree of freedom 39 and significance 0.552 then we have to conclude that there is no significance difference between the two variables.
• The rule is that if the significance value is less than 0.05, there is a significance difference, and if the value is greater than 0.o5, then we have to conclude that there is no significance difference.

One Way ANOVA

• The One Way ANOVA compares the mean of one or more groups based on the one independent variable (factor)
• While using this statistical tool, move all the dependent variables into the box labeled 'Dependent List' and move the independent variable into the box labelled 'Factor'.
• Click on the botton labelled 'options; and check of the boxes for Descriptive and Homogeneity of the Variance.
• Click 'post hoc' botton, if there are equal number of cases in each group choose 'Tukey' if there are not equal numbers of cases in each group, choose 'Bonferroni'.
• The dependent variables should be normally distributed with a Q-Q plot.
• The between groups estimate of variance forms the numerator of the F ratio. The second row corresponds to the within groups estimate of variance (the estimate of error). The within groups estimate of variance forms the denominator of the F ration
• When the significance value is less than 0.05, then we have to reject the Null Hypothesis since the F value is not statistically significant.
• There are two degrees of freedom. The first one is calculated as a-1 where 'a' refers to number of variables. The second degree of freedom is calculated as a(n-1) where 'n' refers to number of cases to be observed.

Pearson Correlation

• The Pearson R Correlation tells us the magnitude and direction of the association between two variables that are on an interval or ratio scale.
• Both variables should be normally distributed.
• SPSS creates a correlation matrix of the two variables. It gives three pieces of information: the correlation coefficient, the significance, and the number of cases (N).
• The correlation coefficient is a number between +1 and -1. This numbers tells us about the magnitude and direction of the association between two variables.
• The magnitude is the strength of the correlation. +1 indicates the strongest positive correlation whereas -1 indicates the strongest negative correlation. If the correlation is 'zero' or very close to it, it shows that there is no correlation between the variables.
• If the correlation is positive, the two variables have positive relationship (as one increases, the other also increases). If the correlation is negative then it shows that the variables have inverse relationships.