All statistical tests described in this manual work by testing null hypotheses, often abbreviated H
_{o}. Null hypotheses are statements that any observed variability or pattern in the data is due to random chance. If p > 0.05 in the statistical test being performed there is no "statistical significance" and the null hypotheses is accepted. If p
< 0.05, there is "statistical significance" and the null hypothesis is rejected.
The research hypothesis is the possible explanation that is of interest to the scientist doing the data analysis. It is almost always different than the null hypothesis. Often when the null hypothesis is rejected, the results support the research hypothesis.
The term alternative hypothesis is commonly used instead of research hypothesis. Often there are several alternative hypotheses each providing a different possible explanation for the observed variability or pattern in the data; each focuses on a different independent variable.
The table below shows the null hypotheses corresponding to the statistical tests described in this manual. Generalized research questions and hypotheses are also included; these questions and hypotheses should always be more specific when referring to specific data sets. See the beginning section of each chapter for specific examples.
Statistical Test 
Null Hypothesis 
Generalized Research Question 
Generalized Research Hypothesis 
tTest

There is no significant difference between the means of the two groups being compared; any difference is solely due to random chance.

Is there a significant difference between the means of the two groups being compared?

The two groups have different mean values. For a onetailed test, a prediction is made about which group should have a larger mean value.

Anova

There is no significant difference among the means of the groups being compared; any differences are solely due to random chance.

Is there a significant difference among the means of the groups being compared?

The groups being compared have different mean values.

Rgression

There is no significant relationship between the dependent and independent variables; the slope of the regression line is not significantly different from zero.

Is there a significant relationship between the dependent and the independent variables?

There is a relationship (usually specified as positive or negative) between the dependent and independent variables.

ChiSquare Test

The observed values are not significantly different from the expected values. In R x C contingency tables, this is synonymous with stating that there is no association between the row and column categories.

Are the observed values different than the expected values?

The observed values are different than the expected values.
