Advanced Research Methods Chapter 15: Statistical Evaluation of Data

Descriptive statistics

Help organize, summarize, and simplify results. Frequency distribution tables (1st column: categories, 2nd: frequency). Histograms or polygons.

Inferential Statistics

Help make generalizations from your sample to a broader population.

Statistic

A summary value that describes a sample.

Parameter

A summary value that describes a population.

Mean

Mathematical average of a set of scores.

Median

Score that divides a distribution in half.

Mode

Most commonly occurring score.

Standard Deviation

Square root of the variance. Describes the average distance from the mean.

Variance

The average squared distance from the mean. Rarely reported in descriptive statistics, but important for the ANOVA.

Using graphs

IV on x-axis and DV on y-axis. Preferred for continuous variables. Ratio or interval data.

Inferential Stats: Hypothesis tests

Statistical procedure. Attempt to distinguish between two explanations for the sample data.

Null Hypothesis

There is no statistical difference between populations.

Alternative Hypothesis

There is a significant statistical difference between populations.

Fail to reject the null hypothesis

Any difference in the results most likely due to chance.

Reject null hypothesis (with some probability)

Supporting alternative hypothesis. Any difference in the results most likely not due to chance. p

Level of significance (a)

Alpha (a) is the level of significance chosen by the researcher to evaluate the null hypothesis. Traditionally, a=0.05 is the cutoff for significance. a=0.01 is a more stringent cutoff.

Type 1 Error

Reject null hypothesis, but be wrong. A false report.

Type 2 Error

Fail to reject null hypothesis, but be wrong. Sample data does not show evidence of a significant effect when a real effect exists in the population. Called a miss.