Chapter 13 – Difference Between Two Parameters

Math 22 Introductory Statistics

Dependent vs. Independent Samples

Independent Samples – Samples that are not related.Dependent Samples – Samples that are related.Classic dependent data examples are “test and re-test” situation or a “before-and-after” situation.

Inferences Concerning The Ratio of Variances

When we compare two samples, one of things that we are concerned with is to see if population variances from each group are the same.Since we do not know what the population variances are, we use sample variances to make this determination.

Inferences Concerning The Ratio of Variances

To see if the population variances are equal, we will use a hypothesis test based on the F – distribution.

Properties of the F-Distribution

The F-distribution is always non-negative (zero or positive)The F-distribution is not symmetric, it is skewed right.Like the t-distribution, the F-distribution is a family of distributions where each member is identified by the degrees of freedom.

Assumptions of the F-Test

The sample data was obtained from two independent populationsThe distributions of both populations are normal.

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:Hypothesis eAlternativ •

:Hypothesis Null •

Two Ways to Determine if the Population Variances are Equal

Method 1: Use the F-TestMethod 2:If the ratio of sample variances is less than 4.Then the population variances are equal If the ratio of sample variances is greater than (or equal to) 4.Then the population variances are not equal

Difference of Means

Difference of Means when Population Variances are equal.Difference of Means when Population Variances are not equal.

Difference of Means: Nonparametric Alternative

If we look at the distributions from both sets of sample data and find both distributions are not normal, we should use a nonparametric approach.If the distributions are similar, we will compare the means, if they are not, then we will compare the medians.

Difference of Means: Nonparametric Alternative

If both distributions appear to be similarWe will compare a difference of meansIf both distributions appear to be different We will compare a difference of medians

Inferences Concerning the Mean Difference Using Two Dependent Samples

When dependent samples are involved, the data is thought of being paired data.Classic examples of paired data are the test/re-test situation and the “before and after” situation.

Other Hypothesis Tests and Confidence Intervals

Hypothesis Test Between Two ProportionsConfidence Interval Between Two MeansConfidence Between Two Proportions