2. WHAT IS THIS TEST?
The t-test assesses whether the means
of two groups are statistically different
from each other. This analysis is
appropriate whenever you want to
compare the means of two groups, and
especially appropriate as the analysis
for the posttest-only two-group
randomized experimental design.
3. WHAT IS THIS TEST?
The test statistic in the t-test is known as
the t-statistic. The t-test looks at the t-
statistic, t-distribution and degrees of
freedom to determine a p value
(probability) that can be used to determine
whether the population means differ. The t-
test is one of a number of hypothesis tests.
To compare three or more variables,
statisticians use an analysis of variance
(ANOVA). If the sample size is large, they
use a z-test. Other hypothesis tests include
the chi-square test and f-test.
4. WHAT IS THIS TEST?
A statistical examination of two population
means.
A two-sample t-test examines whether two
samples are different and is commonly
used when the variances of two normal
distributions are unknown and when an
experiment uses a small sample size. For
example, a t-test could be used to compare
the average floor routine score of the U.S.
women's Olympic gymnastic team to the
average floor routine score of China's
6. Hypothesis for the independent t-test
The null hypothesis for the independent t-test is that the
population means from the two unrelated groups are
equal:
H0: u1 = u2
In most cases, we are looking to see if we can show that
we can reject the null hypothesis and accept the
alternative hypothesis, which is that the population means
are not equal:
HA: u1 ≠ u2
To do this, we need to set a significance level (alpha) that
allows us to either reject or accept the alternative
hypothesis. Most commonly, this value is set at 0.05.
7. What do you need to run an
independent t-test?
In order to run an independent t-
test, you need the following:
One independent, categorical variable that has
two levels.
One dependent variable.
8. Unrelated groups
Unrelated groups, also called unpaired groups or
independent groups, are groups in which the
cases in each group are different. Often we are
investigating differences in individuals, which
means that when comparing two groups, an
individual in one group cannot also be a member
of the other group and vice versa. An example
would be gender - an individual would have to be
classified as either male or female - not both.
12. STEPS
Calculate deviation scores
for each group by subtracting
each score from it's group
mean and squaring it and put
these in the columns "(x-
Mx)2" and "(y-My)2"
16. STEPS
Check to see if t is statistically
significant on probability table
with df = N-2 and p < .05 (N =
total number of scores)
17.
18. PROBLEM
Sam Sleepresearcher hypothesizes that people
who are allowed to sleep for only four hours will
score significantly lower than people who are
allowed to sleep for eight hours on a cognitive
skills test. He brings sixteen participants into his
sleep lab and randomly assigns them to one of
two groups. In one group he has participants
sleep for eight hours and in the other group he
has them sleep for four. The next morning he
administers the SCAT (Sam's Cognitive Ability
Test) to all participants. (Scores on the SCAT
range from 1-9 with high scores representing
better performance).
20. STEP 1
Null hypothesis: People who are allowed to
sleep for only four hours will not score
significantly lower than people who are
allowed to sleep for eight hours on a cognitive
skills test.
Alternative Hypothesis: People who are
allowed to sleep for only four hours will score
significantly lower than people who are
allowed to sleep for eight hours on a cognitive
skills test.
25. STEP 6
According to the t
sig/probability table with df =
14, t must be at least 2.145
to reach p < .05, so this
difference is not statistically
significant
26. INTERPRETATION
Sam's hypothesis was not
confirmed. He did not find a
significant difference between
those who slept for four hours
versus those who slept for eight
hours on cognitive test
performance.
