Analyzing Statistical Inferences July 30, 2001

Inferential Statistics? When? When you infer from a sample to a population Generalize sample results to the larger group

Sampling Error Different samples = different means Must take error into account when inferring to population What if population is the sample? Not sampling error Measurement error

Null Hypothesis Statement of no difference or no relationship. Because of sampling error, it is more accurate to test for no differences/relationships Use statistics to determine the probability that the null hypothesis is true or untrue.

Level of Significance The probability of being wrong in rejecting the null hypothesis. p .05 or p .01 p indicates how often the results would be obtained because of chance.

Type I Error Reject the null hypothesis when it is true. Claim a relationship between variables that does not exist.

Type II Error Fail to reject the null hypothesis when it is not true. Do not indicate a relationship between variables when there is one.

Three Factors affecting the level of significance Difference between groups Greater difference, lower p value Sampling/measurement error Lower error, lower p value Sample size Larger sample, lower p value

What Does it Mean? If null hypothesis is rejected or not: Extraneous variables? Design factors? Internal validity? Statistical significance not necessarily practically significant.

Procedures Parametric statistics Based upon certain assumptions about the data (i.e. normally distributed) Nonparametric statisitics Assumptions about the data cannot be met. Parametric have greater power to detect significant differences.

Common Procedures The t test Compares two means ANOVA Compares two or more means Factorial Analysis of Variance Two or more independent variables analyzed together

Common Procedures ANCOVA Adjusts for pretest difference between groups Univariate One dependent variable analyzed Multivariate Two or more dependent variables analyzed together

Common Procedures Chi-square Tests frequency counts in different categories