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Analysis of Variance (ANOVA)

Chapters 11 - 13

ANOVA:

statistical analysis of experiments with more than 2 groups requires a more complex technique

Most frequently used technique among social and behavioral scientists

Based on assigning the variability of data to different sources

One-Way ANOVA:

Chapter 11

Used to find out if there are any differences among three or more population means (Recall t-test measured two)

Null hypothesis is again that two or more population means in an independent samples design are equal. That is,

Used when treatment levels are independent of each other

NHST with ANOVA:

Populations you are comparing (different treatment groups) may be exactly the same OR one or more of them may have a different mean. These are your null and alternative hypotheses in that order.

At the beginning, we assume that the null hypothesis is true. That is, we believe that the groups have the same mean and any variation is due to chance.

Choose a sampling distribution that shows the probability of various differences among sample means when the null hypothesis is true. For more than 2 sample means, we use the F distribution.

Obtain the data from your populations and do calculations until you have an F value.

NHST with ANOVA:

Compare the F value to the critical value of F in the F distribution Chart in back of book.

Come to a conclusion about null hypothesis. If your F value is less than the number in the chart, you fail to reject the null hypothesis which means that either the null or alternative hypothesis could be true. If your F value is greater than or equal to the value in the chart, we reject the null hypothesis and can state that there is reason to believe there are measurable differences in the means and further investigation may explain these differences (i.e. the differences are not due to chance or randomness)

Tell the story of what the data shows. Rejecting the null hypothesis warrant further study and analysis or discussion. Failing to reject the null hypothesis gives no strong conclusion, but the data is not invalid.

The value F:

For ANOVA, we will be using a new statistic that is called the F value that corresponds to the F-distribution and the chart in the back of the book.

When the null hypothesis is true, this value is close to 1. When it is false, we get a number greater than 1.

Add Data Analysis Pack to Excel

Calculate ANOVA using Excel

Repeated Measures ANOVA

Statistical technique for designs with repeated measures of subjects or groups of matched subjects

Null hypothesis is same as before