1. Exploring Group Differences
Comparing Groups
Exploring Group Differences

2. When to use the t-test
The independent samples t-test is probably the single most widely used test in statistics.
It is used to compare differences between separate groups.
This test can be used to explore differences in naturally occurring groups.
For example, we may be interested in differences of emotional intelligence between males and females.

3. T-test
A t-test is a family of statistical tests designed to determine if differences exist between two groups (and ONLY two groups)
Based on t-scores (which are very similar to z-scores), should tip you off they are based on mean and SD
They test for ‘equality of means’
If the two group means are equal – then there is no difference
3 major types of t-tests
One sample t-test, independent samples t-test, paired- samples t-test

4. In all cases TWO group means are being compared
T-tests
One-sample t-test =
Compares mean of a single sample to known population mean
i.e., group of 100 people took IQ test, are they different from the population average? Do they have above average IQ?
Independent samples t-test =
Compares the means scores of two different groups of subjects
i.e., are science scores different between high fitness and low fitness
Paired-samples t-test =
Compares the mean scores for the same group of subjects on two different occasions
i.e., is the group different before and after a treatment?
Also called a dependent t-test or a repeated measures t-test
In all cases TWO group means are being compared

5. Independent Samples T-Test
Let’s start here, since we need to use this test for our fitness/science question
Independent Samples T-tests:
Used with a two-level, categorical, independent variable– ONLY two groups…
and with one continuous dependent variable
Statistical assumptions – 1) data are normally distributed, 2) samples represent the population, 3) the variance of the two groups are similar (homoscedasticity of variance)
NOTE: Same as correlation/regression – except we no longer have to worry about a ‘linear’ relationship since one of our variables is categorical (high/low fitness)

6. In SPSS

7. SPSS – T-test Move dependent variable to “Test Variable”
Move your independent variable to “Grouping Variable”
Notice, it now has 2 question marks
SPSS needs to know which groups to compare
“Define Groups”

8. SPSS – T-test Recall, ‘male’ was 1, ‘low fitness’ was 2
Manually enter these values into the box
When done, hit “continue’, then ‘ok’

9. T-test results
The first box will contain what you’ve already seen – the mean of the two groups:
Notice, n, mean, standard deviation (ignore SE) for each group
The next box is too big for one screen, so I’ve split it into two pieces…

10. SPSS results - Output
Recall, both groups need to have equal variance (homogeneity of variance, or homoscedasticity)
SPSS tests for this using “Levene’s Test”
This means you do NOT want a p-value < 0.05

11. SPSS results - Output If this Levene’s Test p-value is > 0.05
Equal variances exist, use the top line of the table
If this Leven’s Test p-value is < or = 0.05
Equal variance does not exist, use the bottom line
Becomes harder to find a statistically significant result

12. df – Degrees of Freedom
The table also shows df, or ‘degrees of freedom’
df is important to understand if you are calculating the p-values by hand – we are NOT
All you need to know now is that:
Larger sample size = ↑ df
More groups = ↓ df
You want large df because it reduces your chance of random sampling error (a large sample) and increases the chance you’ll find statistically significant results
This becomes more important beyond t-tests, since we can have several groups (not just 2)

13. df in our example
Notice, the df in our example is 272 (274 subjects minus our two groups (high and low fitness)
If you do not have equal variances, SPSS ‘downgrades’ your df, making it more difficult to find statistically significant results

14. Before we move on…
Remember, we’re trying to determine if the difference between the two groups is real – or due to RSE
What we know so far:
And, the two groups do have equal variance

15. More results Here is the important stuff (remember, using top line):
Our two groups (high/low fitness) had a mean difference of on the science ISAT
239.1 – = 12.2
This difference is statistically significant, p = 0.001

16. Decisions
Questions about t-test results?
HO: There is no difference in science scores between the high fitness and low fitness group
HA: There is a difference in science scores between the high fitness and low fitness group
Decision?
Results: The high fitness group scored higher than the low fitness group on their science ISAT test by points. This difference was statistically significant, t (272) 3.262, p =
Usually report the t value of the test and the degrees of freedom in the paper (from table)

17. One more thing…
Notice in the t-test table that we also were provided with a 95% confidence interval:
95% confidence intervals are a statistic available from most tests, and are related to p-values.
Lower Bound = 4.8, upper bound = 19.5

18. 95% confidence intervals
Confidence intervals are similar to p-values
Remember, p-values indicate probability of random sampling error
We want low p-values, which indicate a low probability of random sampling error
We most often use a p-value cutoff of 0.05, meaning we like to be 0.95 (or 95% confident) that this was NOT due to random sampling error
Confidence intervals give you a similar type of information, but in a more practical sense
Many people prefer confidence intervals over p-values

19. 95% confidence intervals
Remember, in statistics we are using samples to try and figure out information about the population
When we calculate a mean for a sample, we are really trying to understand what the REAL population mean is
But, due to random sampling error, we always know that our sample mean is different from the real population mean
Example – mean IQ score for all 7 billion humans is 100
Sample 1 of 100 humans = 102.1, Sample 2 = 105.3, Sample 3 = 98.2, etc…
Random sampling error