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Chapter 10

# Chapter 10.docx

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University of Guelph

Psychology

PSYC 1010

c

Fall

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Chapter 10- The Independent Samples t Test March 19 th
Conducting an Independent-Samples t Test
- Independent sample t test- used to compare two means for a between-groups
design, a situation in which each participant is assigned to only one condition
- Uses a distribution of differences between means
- Biggest difference that this makes- it takes more work to estimate the standard
error
A Distribution of Differences Between Means
- Looking at overall differences between two independent groups
- We create a distribution of differences between means in order to establish that
the distribution specifies the null hypothesis
6 Steps of an Independent-Samples t Test
1) Identify the populations, distribution, and assumptions
2) State the null and research hypothesis
3) Determine the characteristics of the comparison distribution
There are three degrees of freedom calculations
First- calculate the degrees of freedom for the first sample- subtract 1
from the # of participants in the sample: dfx=N-1
Then- calculate the degrees of freedom for the second sample- subtract
1 from the number of participants in that sample: df y=N-1
Finally- sum the degrees of freedom from the two samples to calculate
the total degrees of freedom: dftota=df x+df y
- Determine the mean and standard error
- A) Calculate the variance
- B) Pool the two estimates of variance
- C) Calculate the variance versions of standard error for each sample
- D) Combine the two variances
Sum the variance versions of standard error:
+
- E) Parallel the two calculations
Calculate the standard deviation of the distribution of
differences between means: √
- Pooled Variance- weighted average of the two estimates of variance-
one from each sample- that are calculated when conducting an
independent-samples t test
- We use all three degrees of freedom calculations (along with variance
estimates) for each sample- in order to calculate pooled variance
- Pooled Variance: ( ) +( )
- Then we calculate the variance version of standard error for each
sample: and for the second sample:
4) Determine critical values, or cutoffs
- Similar to the t tests but use total degrees of freedom:
5) Calculate the test statistic -

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