t test
Inferential Statistics
● Once you have conducted a
two-group experiment, you
need to perform a statistical
test on the data you
gathered.
● The results of this test will
help you decide if the IV was
effective or not.
● Inferential statistical tests
allow you to make an
inference about your results
Unlike the warning on this truck,
– you will decide if your
psychologists view data and
statistical procedures as tools to
results are significant.
help answer research questions
The Relation Between Experimental
Design and Statistics
● Selecting the appropriate design determines
the particular statistical test you will use to
analyze your data.
● Thus, you should decide upon your
experimental design before you start
collecting data to ensure there will be an
appropriate statistical test to analyze your
data.
The Logic of Significance Testing
● The result of an
experiment is
statistically significant is
when it occurs rarely by
chance.
The Logic of Significance Testing
● What is Significant?
– The results of an inferential statistical test tell us
whether the results of an experiment would occur
frequently or rarely by chance.
– Inferential statistics with small values occur
frequently by chance (accept the null hypothesis),
whereas large values occur rarely by chance
(accept the alternative hypothesis).
– Traditionally psychologists say that any event that
occurs by chance alone 5 times or fewer in 100
occasions is a rare event. (i.e., .05 level of
significance).
The Logic of Significance Testing
● Samples and Populations – our interest is not in the
samples we have tested in an experiment, but in
what these samples tell us about the population from
which we drew them. That is, we want to generalize,
or infer, from our samples to the larger population
using the following steps:
– Random selecting a sample from a specified population.
– Randomly assigning participants in the sample to different
groups.
– Apply the manipulation of our independent variable.
– Assuming the groups are significantly different, we
generalize the findings from our experiment to the
population of interest.
Analyzing Two-Group Designs
● The appropriate statistical test is a t test (assuming
you have interval or ratio-level data).
– For a two-independent-groups design, you would use a t
test for independent samples (known as an independent t
test). This test is used when you randomly assign your
participants to the two groups.
– For a two-correlated-groups design, you would analyze the
data with a t test for correlated samples (known as a
dependent t test, within-groups t test, or paired t test). This
test is used when you use repeated measures, matched
pairs, or natural pairs.
The Logic of Significance Testing
● An example of a study
where you could use
the t-test for
independent samples is
examining how long it
takes salesclerks to
wait on customers in
dressy versus sloppy
clothes.
The t Test for Independent Samples
● The formula for an independent samples t test is as
follows:
– Calculating the standard error of the difference between
means takes several steps and requires different formulas
depending on whether the two groups are equal or different
in size.
– We must calculate the standard error of the difference
because we have two groups that contribute to overall
variability rather than only one as when we previously
encountered the standard error of the mean (SEM).
The t Test for Independent Samples
● Once you have calculated the t value, you must
follow several steps in order to interpret its meaning:
– Determine the degrees of freedom (df) involved:
● df = (NA – 1) + (NB – 1)
– Use the degrees of freedom to enter a t table that
contains t values that occur by chance.
– To be significant, the calculated t must be equal or
larger than the one in the table.
– Look for the appropriate level of significance (i.e.,
.05 level) to determine significance.
The t Test for Correlated Samples
● If you used correlated groups such as matched pairs,
repeated measures, or natural pairs for your design,
then you will need to use the t test for correlated
samples.
● Calculating t by hand –
– The formula for the correlated t test is as follows:
● In words, t equals the mean of x minus the mean of
y, divided by the standard error of the deviation
scores.
● df= N-1
Important Reminders
● One-Tailed and Two-Tailed Significance Tests – if
you stated your experimental hypothesis in a
directional manner, then you will use a one-tailed
test of significance. If you used a nondirectional
hypothesis you would use a two-tailed test of
significance.
● Type I and Type II Errors – Type I error (alpha, α)
refers to accepting the experimental hypothesis
when the null hypothesis is in fact true. Rejecting a
true experimental hypothesis is called a Type II error.
The Continuing Research Problem
● Research is a continuous process.
● It is rare for a psychologist to conduct a single
research project and stop at that point because that
one project had answered all the questions about the
particular topic.
● Rather, one experiment usually answers some of
your questions, does not answer others, and raises
new ones for consideration.
