The Independent- Samples t Test Chapter 11

Independent Samples t-Test >Used to compare two means in a between-groups design (i.e., each participant is in only one condition)

Distribution of Differences Between Means

Hypothesis Tests & Distributions

Steps for Calculating Independent 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.

Population 1: People told they are drinking wine from a $10 bottle. Population 2: People told they are drinking wine from a $90 bottle. The distribution: a distribution of differences between means (rather than 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 1: Identify the populations, distribution, and assumptions.

Null hypothesis: On average, people drinking wine they were told was from a $10 bottle give it the same rating as people drinking wine they were told was from a $90 bottle. H 0 : μ 1 =μ 2 Research hypothesis: On average, people drinking wine they were told was from a $10 bottle give it a different rating than people drinking wine they were told was from a $90 bottle. H 1 : μ 1 ≠ μ 2 v Step 2: State the null and research hypotheses.

Calculate the pooled variance and then the standard deviation of the difference. Step 3: Determine the characteristics of the comparison distribution.

Formulae

Additional Formulae

Step 4: Determine critical values, or cutoffs.

Step 5. Calculate the test statistic

Step 6: Make a Decision.

>t(df) = tcalc, p <.05 Use p >.05 if there is no difference between means Use p <.05 if there is a difference between means >t(7) = -2.44, p <.05 Reporting the Statistics

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:

Effect Size

Data Transformations 1. Transform a scale variable to an ordinal variable. 2. Use a data transformation such as square root transformation to “squeeze” the data together to make it more normal. >Remember that we need to apply any kind of data transformation to every observation in the data set.

>When would you use a z test over a t test? >When would you use an independent sample t test? Think of a specific study. >When would you use a paired sample t test? Think of a specific study. Stop and Think