1. Making Inferences From z to t
Statistics

2. A Brief Review of Significance Testing
Revisit Alpha (Type I error)
Type II error
1 – b = Power (Power)

3. Degrees of Freedom X
S = 80 10 10 10 10 10 10 10

4. Selecting the Proper Test
Level of data?
Descriptives vs. Inferentials vs. Nonparemetrics
Comparison? Correlation? Prediction?
Regression vs. Pearson’s R vs. Anova or t
How many groups, variables, or levels?
Anova vs t
Design?
Covariates
Inflated Type I error?
Multivariate vs Univariate tests

5. Student’s t Test Against Population Means
Easy to calculate
When you know the mean and standard deviation of a sample, and wish to compare them to a known population mean
t = (M – m)/s
df = n – 1
If tobt ≤ tcrit, then significant at alpha

6. A Real-Live Example
Tomak et al. (2009) compared MMPIs of a sample of Internet sex offenders (n =48) versus those of a previously studied comparison group of general sex offenders (Summerhill, 2002; unpublished dissertation).
In hindsight, needed to determine if groups differed on demographic variables, such as age.
Did not have Summerhill’s raw data, but did have the mean:
Andjelkovic’s demographics gave us M = 40.67, s = 11.37
Is this a significant difference?
Nope: t(47) = , p > 0.05

7. The Independent t Test
The t vs. population means are convenient, but not terribly powerful. If you have the raw data of independent groups, this formula is much better:

8. The Paired t Test
Similar philosophy as the independent t test, but used when subjects in one group are matched, yoked, used in repeated measures designs, or are otherwise “connected” to subjects in another group.
df = n - 1

9. X1 55 43 51 62 35 48 58 45 54 56 32 X2 48 38 53 58 36 42 55 40 49 50 25 D
SD = D2
SD2 = 7 49 5 25 -2 4 4 16 1 -1 6 36 3 9 5 25 -1 1 4 16 -2 4 7 49 35
235

10. Now, The Fun Part SD/√[(N(SD2) – (SD)2)/n – 1]
35/√[(12(235) – (35)2)/12-1]
35/√[(2820 – 1225)/11]
35/√1595/11
35/√145
35/12.042
2.906
df = 12 – 1 = 11
tcrit = (a = 0.05, 2-tailed)
Reject the null

11. Assumptions…
Normality
Linearity
Interval-level data

12. A Cup of t Test
Determine the best t test to use on the provided data set and interpret the results.

13. t test against population means Hotelling’s T
You have RBANS scores of an elder population that you wish to compare to established norms. Which assessment would be best?
Paired-samples t test
Independent t test
t test against population means
Hotelling’s T
t test against population means

14. What advantage does the t test have over the Analysis of Variance?
Ease of calculation
Greater power
Lower error rate
Ability to compare related groups
Ease of calculation

15. Questions? Thoughts?