Parametric Analyses

• Measurement of the Dependent Variable – (i.e., the variable being analyzed) is on an interval scale
• Observations or Scores are Independent – the score of one individual is not influenced by the score of another
• Population is a Normal Distribution – dependent variable scores are normally distributed – only required if sample size is small (<30)
• Homogeneity of Variance – when two or more populations are being studied they have the same dispersion in their distributions

• Sampling Distribution when the sample standard deviation is used to estimate the population standard deviation
• Degrees of Freedom
• Number of ways the data are free to vary
• Determined by subtracting the number of restrictions placed on the data from the number of scores (often, n-1)
• As degrees of freedom increase, t-distributions become increasingly like normal distributions
• If degrees of freedom exceed 120, normal distribution is used
• Table Lookup – based on the degrees of freedom and the desired level of significance

• Tests the null hypothesis that two or more population means are equal 
• Usually not used for only two means as t-test can be used
• Compares two estimates of variance which are put into a ratio form – F-ratio or F-value
• One-Way ANOVA – only one independent variable is included
• Two-Way ANOVA – two independent variables are included simultaneously
• There is a null hypothesis for each independent variable
• F-ratio computed for each
• F-ratio computed for interaction effect

• Require few, if any, assumptions about the population
• Can be used with ordinal and nominal scale data

• Comparison of observed and expected frequencies
• Contingency Tables – crosstabulations of two variables
• Each variable has two or more categories
• Null hypothesis that there is no relationship between the variables
• Degrees of Freedom – (#rows-1) x (#columns-1)