Hypothesis testing in the REAL
world
t tests: single sample
repeated measures
independent samples
Need for the t test
• Hypothesis testing using z requires knowledge of
population parameters (mean, SD)
• Typical psychological experiments
▫ No knowledge of parameters
▫ Often don’t really care
 e.g. compare effects of IV manipulation in
experimental and control group
▫ Underlying population not critical
▫ Interested in change produced by IV
▫ Typically use ESTIMATES
Estimation
• Best predictor of population mean?
▫ Sample mean
• Best predictor of population SD?
▫ Sample SD
 BUT sample SD will systematically
underestimate true population
variability
 biased estimate
 bias to reject null hypothesis
How do we fix it?
• Adjust the formula for SD
▫ Now we’ll call it s
• n-1
• degrees of freedom
▫ Number of scores in a sample
that are free to vary
• Adjust our comparison
distribution
The t distribution
• Shape-shifter
Using the t table
• df
•p
• cutoff (critical) value
• Things to note:
▫ As df increases, critical value decreases
 Related to sample size
▫ With an infinite sized sample, what are the CVs?
▫ n=30
A sample problem: pg 232
• Conceptual and computational formuli
• SPSS
• Steps in hypothesis testing: hopefulness
following a flood
1. Null hypothesis
Alternative
M(flood) = M(neutral)
M(flood) not= M(neutral)
 Neutral = score of 4
2. Comparison distribution
use estimates from sample
estimated mean
sample mean
estimated SD (s)
s of the sampling distribution
3. Cutoff/critical value
use t table with appropriate df
4. Compute t
5. Decide
6. Tell grandma
A saner approach….
• Computational
formula
• SPSS
Types of t tests
• t test for single sample
▫ Compares sample mean to known or predicted
population mean (e.g. “neutral” hopefulness; no
ESP baseline probability)
• t test for dependent means
▫ Compares samples (from the same people)
collected before and after a given manipulation
 aka – within subjects, repeated measures, paired
samples
• t test for independent means
▫ Compares samples from two unique sets of people
with different levels of the IV for each (EXP,
control groups design)
t test for dependent means
• Difference between one test to the next
▫ Role of IV
▫ If null is true, then difference = ?
▫ pg 238 Communication scores before and after
premarital counseling
1.
2.
3.
4.
5.
6.
State null and alternative
Select appropriate t
Determine critical value
Compute
Decide
Tell your Babushka
t test for independent means
• Pooled estimate of the population SD
▫ Weighted average of s for each sample
▫ pg 279 Effects of writing on health
1.
2.
3.
4.
5.
6.
State null and alternative
Select appropriate t
Determine critical value
Compute
Decide
Tell your Nai nai
Let’s give it a whirl….
1. Siegel (1990) found that elderly people who owned dogs
were less likely to pay visits to their doctors after
upsetting events than those who did not own
pets. Similarly, consider the following data: A sample of
elderly dog owners is compared to a similar group of
elderly persons who do not own dogs. The researcher
records the number of visits to the doctor during the past
year for each person. For the following data, is there a
significant difference in the number of doctor visits
between dog owners and control subjects? Use the .05
level of significance.
CONTROL GROUP: 12, 10, 6, 9, 15, 12, 14
DOG OWNERS: 8, 5, 9, 4, 6
WHAT KIND OF TEST IS THIS???
A psychologist tests a new drug for its painkilling effects. Pain threshold is
measured for a sample of subjects by determining the intensity (in
milliamperes) of electric shock that causes discomfort. After the initial
baseline is established, subjects receive the drug and their pain thresholds
are once again measured. The data are listed below. Do these data indicate
that the drug produces a significant increase in pain tolerance? Use a one
tailed test with the .05 level of significance.
PAIN THRESHOLDS (milliamperes)
without drug
with drug
2.1
3.2
2.3
2.9
3.0
4.6
2.7
2.7
1.9
3.1
2.1
2.9
2.9
2.9
2.7
3.4
3.2
5.3
2.5
2.5
3.1
4.9
A group of students recently complained that all of the statistics
classes are offered in the morning. They claim that they "think
better" later in the day and, therefore, would do better if the course
was offered in the afternoon rather than in the morning. To test this
claim, the instructor scheduled the course at the 2:40 time slot one
semester. The afternoon class is given the exact same course as
during prior semesters, including the same final exam. The
instructor knows that, for previous students the final exam scores
had been normally distributed with a mean of 70. The afternoon
class, with 16 students enrolled, got a mean of 76 with a sample
standard deviation of 8. Did the students in the afternoon section
perform significantly better?
a. Test with p=.05 with a one tailed test.
b. Identify the dependent and independent variables