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…

X = 100 SD = 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

X = 100 SD = 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  H O : ISU students average IQ is 100  H A : 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, 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t  df = 29 (30 – 1 group)  P =  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!!