Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 9.3 | Measuring Effect Size for the t Statistic 287
IN THE LITERATURE
Reporting the Results of a t Test
In Chapter 8, we noted the conventional style for reporting the results of a hypothesis
test, according to APA format. First, recall that a scientific report typically uses the
term significant to indicate that the null hypothesis has been rejected and the term
not significant to indicate failure to reject H 0
. Additionally, there is a prescribed
format for reporting the calculated value of the test statistic, degrees of freedom,
and alpha level for a t test. This format parallels the style introduced in Chapter 8
(page 241).
In Example 9.2 we calculated a t statistic of 3.00 with df = 8, and we decided to
reject H 0
with alpha set at .05. Using the same data, we obtained r 2 = 0.5294 (52.94%)
for the percentage of variance explained by the treatment effect. In a scientific report,
this information is conveyed in a concise statement, as follows:
The infants spent an average of M = 13 out of 20 seconds looking at the attractive face,
with SD = 3.00. Statistical analysis indicates that the time spent looking at the attractive
face was significantly greater than would be expected if there were no preference,
t(8) = 3.00, p < .05, r 2 = 0.5294.
The first statement reports the descriptive statistics, the mean (M = 13) and the standard
deviation (SD = 3), as previously described (Chapter 4, page 121). The next statement
provides the results of the inferential statistical analysis. Note that the degrees of freedom
are reported in parentheses immediately after the symbol t. The value for the obtained
t statistic follows (3.00), and next is the probability of committing a Type I error (less
than 5%). Finally, the effect size is reported, r 2 = 52.94%. If the 80% confidence interval
from Example 9.5 were included in the report as a description of effect size, it would
be added after the results of the hypothesis test as follows:
t(8) = 3.00, p < .05, 80% CI [11.603, 14.397].
Often, researchers use a computer to perform a hypothesis test like the one in Example
9.2. In addition to calculating the mean, standard deviation, and the t statistic for the
data, the computer usually calculates and reports the exact probability (or α level) associated
with the t value. In Example 9.2 we determined that any t value beyond ±2.306
has a probability of less than .05 (see Figure 9.4). Thus, the obtained t value, t = 3.00,
is reported as being very unlikely, p < .05. A computer printout, however, would have
included an exact probability for our specific t value.
Whenever a specific probability value is available, you are encouraged to use it
in a research report. For example, the computer analysis of these data reports an
exact p value of p = .017, and the research report would state “t(8) = 3.00, p =
.017” instead of using the less specific “p < .05.” As one final caution, we note
that occasionally a t value is so extreme that the computer reports p = 0.000. The
zero value does not mean that the probability is literally zero; instead, it means
that the computer has rounded off the probability value to three decimal places and
obtained a result of 0.000. In this situation, you do not know the exact probability
value, but you can report p < .001.