Inferential statistics: Summary

Inferential statistics are used for making inferences from samples to populations. For research purposes, their primary use is to test hypotheses. They provide an estimate of random error (chance). Inferential statistics do NOT correct for sample bias (constant error which results from poor design).

The statistical procedure actually tests the null hypothesis. The null hypothesis is that with respect to the outcome, the samples being compared come from the same population; that any differences in outcome between the groups being compared are due to chance. In other words, the independent variable (treatment or predictor) has no effect on the dependent variable.

The inferential statistic provides a p value - the likelihood of the result if the null hypothesis were true. When the obtained p is less than .05 (or sometimes .01), we reject the null hypothesis. When the null hypothesis is rejected, the alternative, or research hypothesis is accepted.

When the null hypothesis is accepted (p greater than .05), we conclude that the independent (treatment) or predictor variable had no effect on the outcome.

The characteristics of the outcome variable determine which inferential statistic is approriate:

• When comparing or contrasting Means, use ANOVA (either for independent or paired scores).

• If the distribution is skewed and Medians are used instead of Means to describe the samples, then use the grand Median to convert the continuous measures into counts in categories, and use Chi-square to analyze the results.

• If the outcome variable is categorical (rather than on a continuous scale of measurement), use Chi-square.

Steps for testing hypotheses

1. Calculate descriptive statistics
2. Calculate an inferential statistic
3. Find its probability (p value)
4. Based on p value, accept or reject the null hypothesis (H0)
5. Draw conclusion

Self-test#6: Selecting inferential statistics

For reference, see list of Common statistical notations

 Take a look at a video University of Oregon Quant students made for using statistics within the field of psychology.

Terms to know (define each before clicking to see the definition in a pop-up message)

 < > alternative hypothesis ANOVA Chi-square df expected frequencies extraneous factors F or F-ratio factorial H0 H1 inferential statistic level of significance matched groups Median split normal distribution null hypothesis observed frequencies p value paired samples placebo raw data repeated measures research hypothesis sample bias sampling error skewed distribution sources of error t-test Type I error