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

Significance Tests / Hypothesis Testing

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.

We are testing the null hypothesis that the variances forthe two batches are equal.

For example, the alternative hypothesis is

In statistics, if you want to draw conclusions about a null hypothesis H0 (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 H0.

In an applied hypothesis testing

If H0 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 H0 is true. If you get a statistically significant result, you have enough evidence to reject the claim, H0, and conclude that something different or new is in effect (that is, Ha).

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

H1: Research hypothesis (investigator's belief); α =0.05

If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

In this example, the hypotheses are:

Hypothesis testing is the subject of this chapter.

Here we presented hypothesis testing techniques for means and proportions in one and two sample situations. Tests of hypothesis involve several steps, including specifying the null and alternative or research hypothesis, selecting and computing an appropriate test statistic, setting up a decision rule and drawing a conclusion. There are many details to consider in hypothesis testing. The first is to determine the appropriate test. We discussed Z and t tests here for different applications. The appropriate test depends on the distribution of the outcome variable (continuous or dichotomous), the number of comparison groups (one, two) and whether the comparison groups are independent or dependent. The following table summarizes the different tests of hypothesis discussed here.

The research hypothesis is that weights have increased, and therefore an upper tailed test is used.

The null hypothesis usually is a statement

While 0.05 is a very popular cutoff value for rejecting H0, cutoff points and resulting decisions can vary — some people use stricter cutoffs, such as 0.01, requiring more evidence before rejecting H0, and others may have less strict cutoffs, such as 0.10, requiring less evidence.