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:

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)

< >

Chi-square symbol

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


Type I error