The fourth step is to perform the relevant statistical test and acquire a test statistic along with its p or probability value (Iyanaga & Kawada, 1980). The fifth and final step involves making a decision to reject or not reject the null hypothesis based on the test statistic. If the p value is less than the pre-determined level of significance, you would reject the null hypothesis (Voelz 2006).
The role of confidence intervals in hypothesis testing is such that if the confidence interval (which is an interval within which the researcher has a specific degree of confidence that the population parameter of concern exists) does not contain the mean of the null hypothesis distribution then the result is significant (Aron, Coups & Aron 2011 p. 191). The confidence interval then provides limits within which one expects to find the mean or statistical value that is related to the null hypothesis.
The student T-test is used to assess whether the means of two groups are in fact statistically different. Many different types of T-test are employed in hypothesis testing. There is the single sample T-test, where a sample mean is compared to a known population mean with the intent of determining whether the sample has come from that population. There is also the T-test for independent and dependent means. These all test a basic hypothesis that the means of the two groups are different.
The inherent weakness associated with engaging in multiple T-tests for many groups, is that the error associated with each round of testing increases the likelihood of getting a false positive. To compensate for that weakness statisticians utilize Analysis of Variance or ANOVA.
ANOVA assesses the hypothesis that there is a difference between groups and unlike the T-test requires only on round of testing for three or more groups. When ANOVA is used for hypothesis testing, the researcher is able to determine that there is a difference between the groups but does not know which groups are different.
When the researcher is concerned about the relationship between two variables linear correlation is used to measure the relationship and assess whether it is significant. Linear correlation and Pearsons Product Moment Correlation in particular requires that the relationship between the variables be described by a straight line. The hypothesis that is tested is concerned with the change in the dependent variable producing change in the independent. So that the researcher is aware of how closely associated the variables are. In regression on the other hand while the variables are associated; the change in the dependent variable can be predicted by change in the independent variable. Thus, regression analysis is predictive and it is possible to determine the quantum of change in the dependent variable to be observed by a unit of change in the independent variable.
Aron Arthur, Coups Elliot J. & Aron Elaine N. Statistics for the behavioral and social sciences:
A brief course. New York NY Prentice Hall: 2011.
Iyanaga, S. And Kawada, Y. (Eds.). “Statistical Estimation and Statistical Hypothesis Testing.”
Appendix a, Table 23 in Encyclopedic Dictionary of Mathematics. Cambridge, MA:
MIT Press, 1486-1489, 1980.
Ryan, P. (2004). Chapter 3: Inferential Statistics: Estimation and Testing. Retrieved on January
25, 2011 from http://health.adelaide.edu.au/publichealth/staff/ASCIEB_Chapter3.pdf
Voelz, Vincent a. Hypothesis Testing Retrieved from http://www.stanford.edu/~vvoelz/lectures/hypotesting.pdf.