# A small (p)-valueis an indication that the null hypothesis is false.

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable in two or more independent comparison groups. For example, in some clinical trials there are more than two comparison groups. In a clinical trial to evaluate a new medication for asthma, investigators might compare an experimental medication to a placebo and to a standard treatment (i.e., a medication currently being used). In an observational study such as the Framingham Heart Study, it might be of interest to compare mean blood pressure or mean cholesterol levels in persons who are underweight, normal weight, overweight and obese.

## Hypothesis Testing for Means & Proportions

### Hypothesis Testing - Analysis of Variance (ANOVA)

If the absolute value of the t-value is greater than the critical value, you reject the null hypothesis. If the absolute value of the t-value is less than the critical value, you fail to reject the null hypothesis. You can calculate the critical value in Minitab or find the critical value from a t-distribution table in most statistics books. For more information calculating the critical value in Minitab, go to and click *Use the ICDF to calculate critical values*.

### The techniques for hypothesis testing depend on

In the previous example, we set up a hypothesis to test whether a sample mean was close to a population mean or desired value for some soil samples containing arsenic. On this page, we establish the statistical test to determine whether the difference between the sample mean and the population mean is significant. It is called the *t*-test, and it is used when comparing sample means, when only the sample standard deviation is known.

## For example, the alternative hypothesis is

In statistics, if you want to draw conclusions about a null hypothesis H_{0} (reject or fail to reject) based on avalue, you need to set a predetermined cutoff point where only those -values less than or equal to the cutoff will result in rejecting H_{0}.

## In an applied hypothesis testing

If H_{0} is rejected (that is, the -value is less than or equal to the predetermined significance level), the researcher can say she’s found a statistically significant result. A result is if it’s too unlikely to have occurred by chance assuming H_{0} is true. If you get a statistically significant result, you have enough evidence to reject the claim, H_{0}, and conclude that something different or new is in effect (that is, H_{a}).