group differences: the sequel
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GROUP DIFFERENCES: THE SEQUEL
Last time Last week we introduced a few new concepts
and one new statistical test: Testing for group differences Degrees of Freedom 95% Confidence Intervals Independent Samples T-Tests
Tonight we’ll continue this discussion and take a look at the other types of t-tests As we move forward, make sure you understand the
appropriate situation in which to use these tests Front cover of Cronk book, ‘Statistics Coach’ in SPSS
T-tests 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
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?
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
Recall Independent t-tests are used when we have
sampled two, different groups ‘Independent’ is used to describe these tests
because the two groups we sampled are independent of each other No person can be in BOTH groups at the same time Also known as ‘unpaired’ t-tests
One sample t-tests and paired-samples t-tests are similar, but are used for slightly different set-ups
One-Sample T-tests
One-sample t-tests are used when: You have sampled one group and… You want to know if that group is different
from the population The mean of the population has to be known
beforehand
For the sake of example, we’re going to use IQ We’ve discussed this before…
Example with IQ
Imagine I want to know if ISU undergraduate students have ‘above average intelligence’ ‘Above average intelligence’ really means ~ have
an IQ above the population mean/average I’m NOT comparing these students to just
another group, I want to compare these students to EVERYONE in the population (world)
To do this… I take a random sample of 30 ISU undergraduates All 30 student take an IQ test Let’s take another look at IQ in the population…
10085 11570 130
X = 100SD = 15
55 145
Recall that IQ is a standardized intelligence test
The mean of the population is 100
If everyone in the world was tested, the average would be 100
10085 11570 130
X = 100SD = 15
55 145
So, what I really want to know is:Does the average ISU student have an IQ above
100?
The one-sample t-test will make this comparison and provide p
One-Sample T-test
Move the independent variable into the “Test Variable” In this case, our ISU student IQ variable
Now, we provide the population mean in the “Test Value” box so SPSS knows what to test against Recall, the population mean of IQ is 100
Hypotheses
HO: ISU students average IQ is 100 HA: ISU students average IQ is not/is
above 100
Notice that I’m comparing two groups – ISU students The population (the world)
Only using 1 sample – hence the ‘one sample’ t-test
Results
Notice: t, df, p-value Mean difference = ISU Students – Population Mean df = 30 subjects – 1 group = 29 95% Confidence interval does not include 0 We can be confident ISU students have above average IQ
Results in writing
The one-sample t-test revealed that ISU students have an above average IQ, by approximately 4.3 points (t = 2.62, 29). This difference is statistically significant (p = 0.014).
One-Sample T-test
Only used when comparing a sampled group to a known population mean Must use prior research to determine the
population mean
For example, you could NOT use this test to compare ISU students to IWU students Instead, to compare two groups that are
unrelated you should use a…?
One-Sample T-test Example ?’s Is ISU basketball game attendance
different than the MVC league average? Do kids in Bloomington-Normal have a
higher BMI’s than all kids in the US? Do ISU baseball pitchers throw faster
than the average MLB pitcher? Is the average annual cost of living
higher in Bloomington-Normal than the rest of the US?
One-Sample T-test questions?
T-tests 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
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?
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
Paired Samples t-test
So far we’ve only been concerned with cross-sectional analysis of data One measurement at one time point
However, for longitudinal data we have to run a different type of statistical test For example, when we want to know if a variable in
a group has changed from Time 1 to Time 2 (pre to post)
Known as ‘repeated measures’ Because we measured the group once…then repeated
it…
Example of Repeated Measures
Pretend I create a weight loss program called P90Y I want to design a study to see if the program works I only have enough money for 30 people to participate
I have two options from here: 1) I can recruit 30 people, split them into two groups,
and half of them get the P90Y program and half don’t I compare their body weight after half use the program I’d have two groups of 15 instead of one group of 30
My statistical power has decreased, my chance of Type II error has increased (remember, df would equal 28, 30 – 2 groups)
Plus, the two groups of 15 people are different people Ideally, I’d want to compare the same people on and off the
program to remove individual variability
Example of Repeated Measures
Pretend I create a weight loss program called P90Y I want to design a study to see if the program works I only have enough money for 30 people to participate
My other option… 2) I can recruit 30 people and put all 30 of them on the
program Now my statistical power is as strong as possible
Df = 29, 30 - 1 Instead of being compared to another person, now my
subjects will be compared to themselves at the start of the program
This is the true strength of using repeated measures
Drawback The only drawback to using a repeated measures
design in this scenario is that I will not be able to use an independent samples t-test to examine the data
Why? Because the ‘two’ groups I want to test are NOT independent. Comparing 30 people at Time 1 to the same 30 people at
Time 2 They are related You can NOT use a statistical test designed for
independent samples on related groups
Paired Sample T-test
Be careful how you structure your data in SPSS, here is an example from our P90Y experiment
Data File Notice:
The subject line indicates each individual subject
The two variables have been named as “Time 1” and “Time 2” Could also use “pre-” and “post-
test”, etc… As you can see, some subjects
lost weight on the program (some more than others, and some gained weight)
No grouping variable – they are all in the same group!
Notice the box on the left says “Paired Variables” Move over your pre- and post-test
measurements, for the same variable, into the boxes in the same line
Weight at Time 1
Weight at Time 2
Output
Normal t-test output, providing the mean, N, and SD
Notice that SPSS makes it ‘seem like’ you are comparing 2 groups This is why repeated measures statistics should be
used instead of independent samples (it’s like having a bigger sample size)
Output
For paired-samples t-tests, SPSS also provides a correlation between the two variables This correlation should always be strong –
since you’re correlating the same variable within the same people!!
T-test output
‘Mean’ = Mean difference (Time 1 – Time 2) 95% Confidence Interval t df = 29 (30 – 1 group) P = 0.005 P90Y works!!!
Results in writing…
A repeated measures t-test revealed that the group lost an average of 2.9 lbs over the course of the experiment (t = 3.03 (29)). This difference was statistically significant (p = 0.005).
Also…
To use the paired-samples t-test you do not always have to use a repeated measures design (like in our example)
In some instances, researchers select two groups that are ‘matched’ or ‘paired’ based on some specific characteristic This is less common, but it simulates a true
repeated measures test when it is not possible For example…
Paired Samples Alternatives Imagine researchers develop a drug designed to
reduce the number of asthma attacks an asthmatic child has over a 6 month period A true repeated measures design would take a year
6 months without the drug and 6 months with the drug Instead, they gather two groups of children with
asthma and pair them based on characteristics like age, gender, height, asthma severity, etc… Basically, they hand pick a control group to be very
similar to their experimental group
Paired Sample Alternative
Now, they can complete the drug trial in 6 months and still have a suitable control group It is NOT as strong as a true ‘repeated measures’
design, but it is better than nothing You still have to use a repeated measures test –
since you have created two groups that are related to each other (NOT independent)
This is why SPSS uses the term “Paired samples” t-test instead of “repeated measures”. The test can be used for either design.
QUESTIONS on t-tests?
Upcoming…
In-class activity
Homework: Cronk complete 6.2 and 6.4 (you did 6.3 last
week) Holcomb Exercises 40 and 41
More testing for group differences next week! ANOVA!!
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