Paired or Two Sample

A 2-sample t-procedure is used when the data come from two independent, random samples. The variable in question is a difference of means. It is used to determine if two population means are equal.

A matched pairs t-procedure is used when the data is defined in pairs. The variable in question is a mean difference between the two sets of paired data. The two data sets are NOT independent of each other.

Are you ready to determine which procedure to use?

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Suppose you test the computer skills of participants before and after they complete a computer training course. That produces a set of paired observations (Before and After test scores) for each participant. For inference, do you use:

• Paired t-procedures

• Two-sample t procedures

Suppose you randomly sample two different groups of people and test their computer skills. You take one random sample from people who have not taken a computer training course and record their test scores. You take a second random sample from another group of people who have completed the computer training course and record their test scores. For inference, do you use:

• Paired t-procedures

• Two-sample t procedures

In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference.

To test the wear characteristics of two tire brands, A and B, each brand of tire is randomly assigned to 50 cars of the same make and model.

• Paired t-procedures

• Two-sample t procedures

To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music. The month in which each subject listens to music is determined by a coin toss.

• Paired t-procedures

• Two-sample t procedures

A study was designed to compare the effectiveness of two weight-reducing diets. Fifty obese women who volunteered to participate were randomly assigned into two equal-sized groups. One group used Diet A and the other used Diet B. The weight of each woman was measured before the assigned diet and again after 10 weeks on the diet.

• Paired t-procedures

• Two-sample t procedures

To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Ration A and which got Ration B.

• Paired t-procedures

• Two-sample t procedures

Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers.

• Paired t-procedures

• Two-sample t procedures

To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer’s random number generator is used to determine which plots get which fertilizer.

• Paired t-procedures

• Two-sample t procedures