Tests of significance: Statistical significance means there is a good chance that a relationship exists between two variables.
Null hypothesis: States that there is no relationship between any two variables, so statistical effort will be directed to prove that Null hypothesis is likely or not likely. Statistical significance means that null hypothesis is unlikely. Statistical insignificance means that null hypothesis is likely.
Examples of tests of significance for quantitative data: Student t test (parametric), Mann Whitney test (Non parametric). Paired t test (parametric), Wilcoxon test (Non parametric). Analysis of variance (annova), Pearson correlation.
Examples of tests of significance for qualitative data: Chi square: Parametric & expected cells more than 5. Fisher Exact test: Parametric & expected cells less than 5. Mc Nemar test (Non-parametric), Z test, Spearman correlation.
The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.
Null hypothesis (H0): The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
Alternative Hypothesis (H1)
The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.
Alpha risk is the risk of incorrectly deciding to reject the null hypothesis. If the confidence interval is 95%, then the alpha risk is 5% or 0.05. Alpha risk is also called False Positive, Type I Error, or “Producers Risk”.
Beta risk is the risk that the decision will be made that a difference does not exist when there actually is.
Chi square test: Used for qualitative data with No. & %. The figures available in the cells of the table are the observed figures (O). It is better to avoid using chi square if any number in the observed cells is less than 6. The expected figure ( E ) for each cell is required to be calculated. It equals: total row x total column / grand total. The equation of chi square is ( χ2 ) = Ʃ [( O – E )2 /E]
Calculate the degree of freedom (df) which equals ( r – 1 ) x ( c – 1 ) where r is the number of rows and c is the number of columns. Go to chi square table, column of df and record the value of chi corresponding to the estimated df. This chi is the tabulated chi. Compare the calculated chi with the tabulated one, if the calculated is more, the result is significant, if equal or less, insignificant.
How to use chi square table: According to the degree of freedom go to the value of the chi under the column titled 0.050, this value is the tabulated chi.