The first table, (Group Statistics) shows descriptive ...



The first table, (Group Statistics) shows descriptive statistics for the two groups (low-stress and high-stress) separately. Note that the means for the two groups look somewhat different. This might be due to chance, so we will want to test this with the t test in the next table.

The second table, (Independent Samples Test) provides two statistical tests. In the left two columns of numbers, is the Levene’s Test for Equality of Variances for the assumption that the variances of the two groups are equal (i.e., assumption of homogeneity of variance). NOTE, this is not the t test; it only assesses an assumption! If this F test is not significant (as in the case of this example), the assumption is not violated (that is, the assumption is met), and one uses the Equal variances assumed line for the t test and related statistics. However, if Levene’s F is statistically significant (Sig < 0.05), then variances are significantly different and the assumption of equal variances is violated (not met). In that case, the Equal variances not assumed line would be used – for which SPSS adjusts the t, df, and Sig. as appropriate.

Also in the second table… we obtain the needed information to test the equality of the means. Recall that there are three methods in which we can make this determination.

Method One (most commonly used): comparing the Sig. (probability) value (p = .022 for our example) to the a priori alpha level (( = 0.05 for our example). If p < ( – we reject the null hypothesis of no difference. If p > ( – we retain the null hypothesis of no difference. For our example, p < (, therefore we reject the null hypothesis and conclude that the low-stress group (M = 45.20) talked significantly more than did the high-stress group (M = 22.07).

Method Two: comparing the obtained t statistic value (tobt = 2.430 for our example) to the t critical value (tcv). Knowing that we are using a two-tailed (non-directional) t test, with an alpha level of 0.05 (( = 0.05), with df = 28, and looking at the Student’s t Distribution Table – we find the critical value for this example to be 2.048. If |tobt| > |tcv| – we reject the null hypothesis of no difference. If |tobt| < |tcv| – we retain the null hypothesis of no difference. For our example, tobt = 2.430 and tcv = 2.048, therefore, tobt > tcv – so we reject the null hypothesis and conclude that there is a statistically significant difference between the two groups. More specifically, looking at the group means, we conclude that the low-stress group (M = 45.20) talked significantly more than did the high-stress group (M = 22.07).

Method Three: examining the confidence intervals and determining whether the upper (42.637 for our example) and lower (3.630 for our example) boundaries contain zero (the hypothesized mean difference). If the confidence intervals do not contain zero – we reject the null hypothesis of no difference. If the confidence intervals do contain zero – we retain the null hypothesis of no difference. For our example, the confidence intervals (+3.630, +42.637) do not contain zero, therefore we reject the null hypothesis and conclude that the low-stress group (M = 45.20) talked significantly more than did the high-stress group (M = 22.07).

Note that if the upper and lower bounds of the confidence intervals have the same sign (+ and + or – and –), we know that the difference is statistically significant because this means that the null finding of zero difference lies outside of the confidence interval.

Calculating an Effect Size: Since we concluded that there was a significant difference between the average amount of time spent talking between the two groups – we will need to calculate an effect size to determine the magnitude of this significant effect. Had we not found a significant difference – no effect size would have to be calculated (as the two groups would have only differed due to random fluctuation or chance).

To calculate the effect size for this example, we will use the following formula:

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Where, t = 2.43

N1 = 15

N2 = 15

Substituting the values into the formula – we find:

[pic] = .89

Independent-Samples T-Test Example

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Drop-Down Syntax for Independent-Samples T-Test Example

T-TEST

GROUPS=stress(1 2)

/MISSING=ANALYSIS

/VARIABLES=talk

/CRITERIA=CIN(.95) .

Alternative Syntax for Independent-Samples T-Test Example

t-test / groups = stress (1, 2) / variables = talk.

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