Chapter 11 Flashcards
What is an independent-samples t-test used for?
Chap.11, Pg. 262
■■An independent-samples t test is used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition.
When is an independent-samples t test used?
MASTERING THE CONCEPT pg. 263
11.1: An independent-samples t test is used when we have two groups and a between-groups research design; that is, every participant is in only one of the two groups.
What is Pooled Variance?
Chap.11, Pg. 268
■■Pooled variance is a weighted average of the two estimates of variance—one from each sample—that are calculated when conducting an independent-samples t test.
What are the calculations for degrees of freedom for an independent-samples t test?
MASTERING THE FORMULA Pg. 268
11-1: There are three degrees of freedom calculations for an independent-samples t test. We calculate the degrees of freedom for each sample by subtracting 1 from the number of participants in that sample:
dfX = N -1 and dfY = N - 1.
Finally, we sum the degrees of freedom from the two samples to calculate the total degrees of freedom: dftotal = dfX + dfY
How do we calculate pooled variance?
MASTERING THE FORMULA Pg. 268
11-2: We use all three degrees of freedom calculations, along with the variance estimates for each sample, to calculate pooled variance:
s2pooled = (dfX / dftotal)s2X + (dfY / dftotal)s2Y
This formula takes into account the size of each sample. A larger sample has larger degrees of freedom in the numerator, and that variance therefore has more weight in the pooled variance calculations.
How do we calculate the t statistic for a two sample between-groups design?
MASTERING THE FORMULA Pg. 268
11-3: The next step in calculating the t statistic for a two-sample, between-groups design is to calculate the variance version of standard error for each sample by dividing variance by sample size. We use the pooled version of variance for both calculations. For the first sample, the formula is:
s2MX = s2pooled / NX
For the second sample, the formula is:
s2MY = s2pooled / NY
Note that because we’re dealing with variance, the square of standard deviation, we
divide by N, the square of √N —the denominator for standard error.
How do we calculate the variance of the distribution of differences between means?
MASTERING THE FORMULA Pg. 269
11-4: To calculate the variance of the distribution of differences between means, we sum the variance versions of standard error that we calculated in the previous step:
s2difference = s2MX + s2MY
How do we calculate the standard deviation of the distribution of differences between means?
MASTERING THE FORMULA Pg. 269
11-5: To calculate the standard deviation of the distribution of differences between means, we take the square root of the previous calculation, the variance of the distribution of differences between means. The formula is:
sdifference = √s2difference
How do we calculate the test statistic for an independent-samples t test ?
MASTERING THE FORMULA Pg. 269
11-6: We calculate the test statistic for an independent-samples t test using the following formula:
t = (MX – MY) – (μ¬X – μ¬Y) / sdifference
We subtract the difference between means according to the null hypothesis, usually 0, from the difference between means in the sample. We then divide this by the standard deviation of the differences between means. Because the difference between means according to the null hypothesis is usually 0, the formula for the test statistic is often abbreviated as:
t = (MX – MY) / sdifference
How do we calculate the upper and lower bounds of the confidence interval in a independent samples t-test?
MASTERING THE FORMULA Pg. 272
11-7: The formulas for the upper and lower bounds of the confidence interval are
(MX - MY)upper = t(sdifference) + (MX - MY)sample and
(MX - MY)lower = -t(sdifference) +(MX - MY)sample respectively.
In each case, we multiply the t statistic that marks off the tail by the standard error for the differences between means and add it to the difference between means in the sample. Remember that one of the t statistics is negative.
Explain the use of the independent samples t-test?
Chapter 11, Pg. 271
> When we conduct an independent-samples t test, we cannot calculate individual difference
scores. That is why we compare the mean of one sample with the mean of the other sample.
The comparison distribution is a distribution of differences between means.
We use the same six steps of hypothesis testing that we used with the z test and with the
single-sample and paired-samples t tests.
Conceptually, the t test for independent samples makes the same comparisons as the other
t tests. However, the calculations are different, and critical values are based on degrees of
freedom from two samples.
Is it possible to calculate a confidence interval for an independent samples t-test?
MASTERING THE CONCEPT Pg. 272
11.2: As we can with the z test, the single-sample t test, and the paired-samples t test, we can determine a confidence interval and calculate a measure of effect size—Cohen’s d—when we conduct an independent-samples t test.
How do we calculate Cohen’s d for a between-groups design?
MASTERING THE FORMULA Pg. 275
11-8: For a two-sample, between-groups design, we calculate Cohen’s d using the following
formula:
Cohen’s d = (MX – MY) – (μ¬X – μ¬Y) / spooled
The formula is similar to that for the test statistic in an independent-samples t test, except that we divide by pooled standard deviation, rather than standard error, because we want a measure of variability not altered by sample size.
How does a square root transformation reduce skew?
Chap.11, Pg. 276
■■A square root transformation reduces skew by compressing both the negative and positive
sides of a skewed distribution.
Explain the use of a confidence interval in an independent samples t test.
Chapter 11, Pg. 277
> A confidence interval can be created with a t distribution around a difference between means.
> We can calculate an effect size, Cohen’s d, for an independent-samples t test.
> When the sample data suggest that the underlying population distribution is not normal and the sample size is small, it is sometimes possible to use data transformation to transform skewed data into a more normal distribution.
