PSYC1010 – Units 6&7
Hypothesis Testing – One and Two Samples
What is the t-test?
Statistical test that is based on the student’s t-distribution
Used to Compare
o A group mean against a “test statistic”
o Means between two different groups
o Means within one group with 2 measurements
z-test vs. t-test
o Use z-test when population standard deviation is known
o There is ONE z-distribution
o There are MANY t-distributions
T-Distribution
Variability decreases with larger sample sizes
t-distribution curves more platykurtic
t-distribution depends on sample size
t-test vs. z-test
One-Sample z-test
Determining if a sample is representative of the population
z = x̄ - μ / X̅
One-Sample t-test
Determining if a sample is representative of the population
tdf = x̄ - μ / sx̄
Hypothesis Testing
1. State null hypothesis
2. State alternative hypothesis
3. Choose α level and one or two-tailed
4. State rejection and accept rule
5. Compute appropriate statistic
6. Make decision by applying rejection / accept rule
7. Write conclusion in context of study
The z-test
One-sample t-test
Research Question
o Does perceived exertion ratings (out of 10) correspond to the weight lifted? In
other words, will subjects rate a “2” when lifting a load of 20% of their individual
1RM? How about a “5” for a 50% 1RM load?
Population
Hypothesis Testing – One and Two Samples
What is the t-test?
Statistical test that is based on the student’s t-distribution
Used to Compare
o A group mean against a “test statistic”
o Means between two different groups
o Means within one group with 2 measurements
z-test vs. t-test
o Use z-test when population standard deviation is known
o There is ONE z-distribution
o There are MANY t-distributions
T-Distribution
Variability decreases with larger sample sizes
t-distribution curves more platykurtic
t-distribution depends on sample size
t-test vs. z-test
One-Sample z-test
Determining if a sample is representative of the population
z = x̄ - μ / X̅
One-Sample t-test
Determining if a sample is representative of the population
tdf = x̄ - μ / sx̄
Hypothesis Testing
1. State null hypothesis
2. State alternative hypothesis
3. Choose α level and one or two-tailed
4. State rejection and accept rule
5. Compute appropriate statistic
6. Make decision by applying rejection / accept rule
7. Write conclusion in context of study
The z-test
One-sample t-test
Research Question
o Does perceived exertion ratings (out of 10) correspond to the weight lifted? In
other words, will subjects rate a “2” when lifting a load of 20% of their individual
1RM? How about a “5” for a 50% 1RM load?
Population
