Statistical Analyses

What we know:

Means & Standard Deviations

• An appropriate way to state descriptive statistics

• Fundamental measures to describe typical or average group performance

• Mean describes the middle of a set of scores and standard deviation is a measure of the average distance from the mean

Independent Measures t-test

• Compares two means of two separate samples

• Evaluates two separate samples and calculates their mean difference

• Must reference the t distribution table to determine if the mean difference is a significant difference

• Can only be two means

• Each participant takes part in only one condition (between-subjects design)

• Less internal validity than a repeated measures t-test

• Uses pooled variance

Repeated Measures t-test

• Same individuals in both conditions (within-subjects design)

• Repeated measures design must use counterbalancing to deal with time-related factors and order effects

• The difference score for each participant enters into the analysis instead of the raw scores. Enter raw scores into SPSS. SPSS automatically calculates the difference scores.

• Less variance due to individual differences.

• Might have less external validity than an independent measures design IF order and carryover effects are not controlled.

Single Factor Independent Measures ANOVA

• Use for a between-subjects design with two or more separate samples or treatment conditions

• If three treatment conditions, must use an ANOVA. An independent measures t-test can only compare two treatment conditions.

• Use a stacked format in SPSS. All scores from the dependent variable are in one column. Will then need a second column to specify which level of the independent variable the participant received.

• Computes an F statistic

• When making a decision about significance, we look for p to be less than .05 (very unlikely for this result to occur by chance alone).

Single-Factor Repeated Measures ANOVA

• Use for a repeated measures (within subjects) design. This means that each participant participates in all levels of the independent variable.

• In order to get a significant difference, there needs to be a consistent difference in a particular direction.

• Has more power than an independent measures ANOVA--is more likely to detect a treatment effect if one is present

• This analysis eliminates variability due to individual differences

• If you retain the null, you do not have to do a post hoc test

Two Factor Independent Measures ANOVA or Factorial ANOVA

• Two independent variables--each level of variable A is combined with each level of variable B. Each participant contributes a score in only one treatment condition. Each cell in the matrix represents a separate sample. For a 2 x3 design there would be 6 cells: A1B1, A1B2, A1B3, A2B1, A2B2, A2B3

• The overall analysis combines three separate hypothesis tests in one analysis--2 main effects and an interaction

• With a significant interaction in the overall analysis, follow up with a test for simple main effects--this tests for differences within each row or column of the AB matrix.

Chi-Square Test

• Individuals are classified into non-numerical categories on a nominal or ordinal scale
• Data are reported as frequencies--how many participants fall into each category
• Chi-Square test for goodness of fit--individuals are classified on ONE variable and then compared to a pre-existing distribution
• Chi-Square test for Independence--Each individual's category membership is determined by their membership on TWO variables and then the test analyzes whether the distribution across one variable is a different pattern then the distribution across the other level of the independent variable. For example, if we classify every respondent according to overall grade average (A, B, C, D, or F) and gender (Male or Female).  A test for independence would allow us to determine whether the pattern of frequencies across grade categories for females is the same as the pattern of frequencies across grades for males.