Hypothesis Testing: The Basics

HYPOTHESIS TESTING involves using statistical techniques to determine whether there is enough evidence to support the hypothesis.  Hypothesis testing helps researchers and analysts make decisions about the validity of their assumptions or claims; thus, it plays a critical role in allowing researchers and administrators to:

• report sample findings with any manner of certainty
• make inferences/draw conclusions about a population based on sample data

We never “prove” anything in social sciences; the best that we can say is that the results support our hypothesis within a pre-determine level of statistical certainty (usually, the .05 significance level or 95% confidence interval).

How Hypothesis Testing Works

Hypothesis testing involves:

1. Developing a research question
2. Operationalizing your concepts and identifying the dependent and independent variables to include in the analysis
3. Formulating research, null, and alternative hypotheses
4. Selecting an appropriate significance level to serve as the threshold for rejecting the null hypothesis (usually, α = 0.10, 0.05, or 0.01)
5. Analyzing data to make a decision about the validity of the hypotheses

We always start research by assuming the null hypothesis is correct — in other words, that there is no relationship between our dependent and independent variables.  From this starting point, our job is to create models based on theory and existing knowledge, run these models, interpret the results, and report the findings.

When we engage in hypothesis testing, we either:

• REJECT THE NULL (meaning there is a relationship between the two variables)
• FAIL TO REJECT THE NULL (meaning there is no relationship between the two variables)

To determine whether we should reject the null or fail to reject the null, we first need to calculate the appropriate TEST STATISTIC; this depends on the type of data and the hypothesis being tested.  Examples of test statistics include the t-test, the z-test, and the differences in means test for two or more groups (i.e., ANOVA, which stands for analysis of variance). Then, based on the chosen significance level (ex: α = 0.05), we need to identify either the P-VALUE (i.e., the probability of obtaining the observed results, or more extreme results, if the null hypothesis is true) or the CRITICAL VALUE (i.e., the cutoff value that defines the REJECTION REGION for the null hypothesis).  From there, we would either:

• compare the test statistic to the critical value (if using the critical value approach); if the absolute value of the test statistic is smaller than the critical value, the test statistic falls into the rejection rage, and we would reject the null hypothesis
• compare the p-value to the significance level (if using the p-value approach); if the p-value is less than or equal to the significance level, we would reject the null hypothesis

Rejecting the null hypothesis within our predetermined level of confidence indicates that we found a statistically significant relationship between two or more variables.