The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups (although you tend to only see it used when there are a minimum of three, rather than two groups).

The null hypothesis in ANOVA is always that there is no difference in means. The research or alternative hypothesis is always that the means are not all equal and is usually written in words rather than in mathematical symbols.

The only difference between one-way and two-way ANOVA is the number of independent variables. A one-way ANOVA has one independent variable, while a two-way ANOVA has two.

A one-way ANOVA hypothesis test follows the same step-wise procedure as other hypothesis tests.

1. Step 1State the null hypothesis H0 and alternative hypothesis.
2. Step 2Decide on the significance level, α.
3. Step 3Compute the value of the test statistic.
4. Step 4Determine the p-value.

When the p-value is less than the significance level, the usual interpretation is that the results are statistically significant, and you reject H 0. For one-way ANOVA, you reject the null hypothesis when there is sufficient evidence to conclude that not all of the means are equal.

The alternative hypothesis is that “the population means are not all equal”. The next step in standard inference is to select a statistic for which we can compute the null sampling distribution and that tends to fall in a different region for the alternative than the null hypothesis.

The F value in one way ANOVA is a tool to help you answer the question “Is the variance between the means of two populations significantly different?” The F value in the ANOVA test also determines the P value; The P value is the probability of getting a result at least as extreme as the one that was actually observed.

variation between sample means

When performing a one-way ANOVA using statistical software, you will be given the p-value in the ANOVA source table. If performing a one-way ANOVA by hand, you would use the F distribution. If p ≤ α reject the null hypothesis. If fail to reject the null hypothesis.

H0: The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0….An appropriate alternative hypothesis is:

1. p = 0.20.
2. p > 0.20.
3. p < 0.20.
4. p ≤ 0.20.