1. Introduction to the t Test Part 1: One-sample t test
Chapter 7
Introduction to the t Test
Part 1: One-sample t test
Sept. 25, 2014

2. t Test for a Single Sample
Z test requires that you know  from pop
Use a t-test when you don’t know the population standard deviation.
One sample t-test:
Compare a sample mean to a population with a known mean but an unknown variance

3. Hypothesis testing procedure for t-test
Same general procedure:
Assume null hypothesis is true, relative to an alternate (research hypothesis)
Compute observed t statistic from sample data based on sampling distribution of the mean
Determine cutoff point (now a critical t) in comparison distribution based on 
Reject the null hypothesis if your observed t value falls in critical region
|t observed| > |t critical|

4. One–sample t Test
Must estimate the population variance from the sample scores
Unbiased estimate of the population variance (S2)
Sum of squared
deviations
Use N-1 to make
S2 bigger than sample

5. t Test for a Single Sample
Degrees of freedom
Number of scores that are
“free to vary”
Formula for S2 using degrees of freedom
Note: S2 indicates we estimated this from a sample
( always indicates population info)

6. t Test for a Single Sample
Also need to find standard deviation of distribution of means (SM)
The variance of the distribution of means
The standard deviation of the distribution of means

7. t Test for a Single Sample
For t-tests, relevant comparison distribution is t distribution (not the normal curve used before in z test)
The t distribution

8. One-sample t Test State null & research hypotheses
Assuming null is true, compute observed t statistic for your sample mean
Find correct critical t value based on your df
When do we reject the null?

9. Note on t-table
When > 30 df, critical values only given for 35, 40, 45 df, etc.
If your df are in between these groups, be more conservative and use the lower df
Do example in class…

10. One Sample t-test in SPSS
Use menus for:
Analyze  Compare Means  One sample t
Gives pop-up menu…need 2 things:
select variable to be tested/compared to population mean (use “self-esteem”)
Notice “test value” window at bottom. Enter the population/comparison mean here (use x.xx from past semester)
Hit OK, get output and find sample mean, observed t, df, significance value (if < .05, reject null)