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

- Calculate descriptive statistics
- Calculate an inferential statistic
- Find its probability (
*p*value) - Based on
*p*value, accept or reject the null hypothesis (H0) - Draw conclusion

ordinal
level of measurement - refers to order; indicates direction. |

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)