The Paired-Samples t Test Chapter 10

Paired-Samples t Test >Two sample means and a within-groups design >The major difference in the paired- samples t test is that we must create difference scores for every participant

Distribution of Differences Between Means

Steps for Calculating Paired Sample t Tests >Step 1: Identify the populations, distribution, and assumptions. >Step 2: State the null and research hypotheses. >Step 3: Determine the characteristics of the comparison distribution. >Step 4: Determine critical values, or cutoffs. >Step 5: Calculate the test statistic. >Step 6: Make a decision.

Example of Paired Sample t Test Study of how 15 volunteers performed on a set of tasks under two conditions: Using a 15-inch computer monitor compared to using a 42-inch monitor

Step 1: Identify the populations, distribution, and assumptions. Population 1: People doing tasks using a 15-inch monitor. Population 2: People performing tasks using a 42-inch monitor. The distribution: a distribution of mean difference scores. Assumptions: The participants were not randomly selected so we must be cautious with respect to generalizing our findings. We do not know whether the population is normally distributed.

Step 2: State the null and research hypotheses. Null hypothesis: People who use a 15-inch screen will complete a set of tasks in the same amount of time, on average, as people who use a 42-inch screen. H 0 : μ 1 =μ 2 Research hypothesis: People who use a 15-inch screen will complete a set of tasks in a different amount of time, on average, from people who use a 42-inch screen. H 1 : μ 1 ≠ μ 2

Step 3: Determine the characteristics of the comparison distribution. M difference = -11

Step 4: Determine the critical values, or cutoffs.. df = N - 1 = = 4 The critical values, based on a two-tailed test and a p level of 0.05, are and

Step 5: Calculate the test statistic. Step 6: Make a decision. Reject the null hypothesis.

Beyond Hypothesis Testing >Just like z tests, single-sample t tests, and paired-samples t tests, we can calculated confidence intervals and effect size for independent-samples t tests

Steps for Calculating CIs >Step 1. Draw a normal curve with the sample difference between means in the center. >Step 2. Indicate the bounds of the CI on either end, writing the percentages under each segment of the curve. >Step 3. Look up the t values for lower and upper ends of the CIs in the t table. >Step 4. Convert the t values to raw differences. >Step 5. Check the answer.

A 95% Confidence Interval for Differences Between Means, Part I

A 95% Confidence Interval for Differences Between Means, Part II

A 95% Confidence Interval for Differences Between Means, Part III

Effect Size >Used to supplement hypothesis testing >Cohen’s d:

Order Effects >How a participant’s behavior changes when the dependent variable is presented for a second time. >For the computer monitor study: The time it took them to complete the series of tasks was recorded under each condition. Can you spot the confound?

Counterbalancing >Minimizes order effects by varying the order of presentation of different levels of the independent variable from one participant to the next. In the computer monitor example, what could we change? >Measures such as this can reduce order effects in within-groups research designs.