Transcript on t tests - Educational Research Basics by Del Siegle

By Del Siegle, PhD
[email protected]
www.delsiegle.info
Press the space bar or your mouse
button to work through this
introduction on t tests.
c. 2002 Del Siegle
(This presentation may be used for instructional purposes)
Suppose we conducted a study to compare two
strategies for teaching spelling.
Group A had a mean score of 19. The range of scores
was 16 to 22, and the standard deviation was 1.5.
Group B had a mean score of 20. The range of scores
was 17 to 23, and the standard deviation was 1.5.
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c. 2002 Del Siegle
How confident can we be that the difference we
found between the means of Group A and Group B
occurred because of differences in our reading
strategies, rather than by chance?
A t test allows us to compare the means of two groups and
determine how likely the difference between the two means
occurred by chance when there was no difference in population
from which the sample was drawn.
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The calculations for a t test requires three pieces of
information:
- the difference between the means (mean difference)
- the standard deviation for each group
- and the number of subjects in each group.
All other factors being equal, large differences
between means are less likely to occur by chance
than small differences.
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The size of the standard deviation also influences the
outcome of a t test.
Given the same difference in means, groups with
smaller standard deviations are more likely to report a
significant difference than groups with larger
standard deviations.
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From a practical standpoint, we can see that smaller
standard deviations produce less overlap between the
groups than larger standard deviations. Less overlap
would indicate that the groups are more different from
each other.
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The size of our sample is also important. The
more subjects that are involved in a study,
the more confident we can be that the differences we
find between our groups did not occur by chance.
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Once we calculate the outcome of the t test (which
produces a t-value), we check that value (with the
appropriate degrees of freedom) on a critical value table
(a process similar to what we did for correlations) to
determine how likely the difference between the means
occurred by chance.
I have created an excel spreadsheet which does these
calculations and provides this information. I have also
created a PowerPoint presentation that demonstrates
how to use the Excel spreadsheet.
c. 2002 Del Siegle
The above process can be accomplished with a computer
statistical package which calculates the means and
standard deviations of both groups, the mean difference,
the standard error of the mean difference, and a p-value
(probability of the mean difference occurring by chance).
There are three types of t tests and each is calculated
slightly differently.
An independent t test compares the averages of two
samples that are selected independently of each other
(the subjects in the two groups are not the same people).
There are two types of independent t tests: equal
variance and unequal variance.
c. 2002 Del Siegle
A correlated (or paired) t test is concerned with the
difference between the average scores of a single sample
of individuals who is assessed at two different times
(such as before treatment and after treatment) or on two
different measures. It can also compare average scores
of samples of individuals who are paired in some way
(such as siblings, mothers and daughters, persons who
are matched in terms of a particular characteristics).
An equal variance (pooled variance) t test is used when
the number of subjects in the two groups is the same
OR the variance of the two groups is similar.
c. 2002 Del Siegle
An unequal variance (separate variance) t test is used
when the number of subjects in the two groups is
different AND the variance of the two groups is different.
How do we
determine which
t test to use…
Paired t test
(Dependent t-test;
Correlated t-test)
Are the scores for the two
means from the same subject
(or related subjects)?
Yes
No
Are there the same
number of people in
the two groups?
No
Yes
Equal Variance
Independent t test
(Pooled Variance
Independent t-test)
Are the variances of
the two groups
different?
Equal Variance
Independent t test
(Pooled Variance
Independent t test)
(Significance Level
for Levene (or F-Max)
is p >.05
Yes
(Significance Level
for Levene (or F-Max)
is p <.05
Unequal Variance
Independent t-test
(Separate Variance
Independent t test)
c. 2002 Del Siegle
No