Transcript Many Possible Explanations Exist

```Two Sample Tests
When do use independent
When groups are inherently different
Normal controls vs. patient
Men vs. Women
When participation in one condition contaminates
measurement of other condition
Conjunction fallacy (Earthquakes)
Reasoning problems
Two Sample T-test
Independent Means
Two-tailed:
H0 : μ1 = μ2
HH10 : μ1 μ2
One-tailed:
H0 : μ1 <= μ2
H0 : μ1 >= μ2
H1 : μ1 > μ2
H1 : μ1 < μ2
Two Sample Tests
Which distributions to use?
Related (dependent)
(Observed Value) – (Expected value under Null Hypothesis)
__________________________________________________
Standard error of null hypothesis of mean differences
Unrelated (independent)
(Observed Value) – (Expected value under Null Hypothesis)
__________________________________________________
Standard error of null hypothesis (comparison) distribution
= ????
Independent t-test
Null hypothesis distribution
Comparing two different population means
Are these means from same population?
To answer this, we need to know:
What should a difference of these means be? 0.
But how much variability should there be between a
difference of means? Hmmm..
Comparing a difference between these means requires a
distribution of the difference of means
Independent t-test
Distribution of the difference of means
Three steps
Step 1: Find how much scores vary.
Step 2: Use central limit theorem to find out how much means vary.
Step 3: Find out how much difference of means vary
Independent t-test
Finding how much scores vary
If we had one sample, we could estimate how population varies by
using sample σ (same as sample estimate of population σ)
But we have two samples, so how do we combine two estimates
of population standard deviation?
By using them both.
Should they both be used equally?
Are they both equally good estimates?
What is one is larger sample size?
Answer: Use larger sample size estimates more than smaller
sample size estimates
Independent t-test
Step 1: Pooled variance
Pooled variance is the combination of both sample standard
variances weighted by the degrees of freedom (n-1).
Larger sample is weighted more. Smaller sample is weighted less.
Step 2: Variance of Means
Step 3: Variance of
Difference of Means
Step 3: Variance of Difference of Means
Group 1 (California): n=36
Group 2 (USA): n = 9
Group 1 is 4 times as large, so mean distribution is twice as
skinny.
Group 1 (California): n=36
Group 2 (USA): n = 9
Independent t-test
(Observed Value) – (Expected value under Null Hypothesis)
__________________________________________________
Independent t-test
(μ1 - μ2 ) – (0)
__________________________________________________
Independent t-test
μ1 - μ2
__________________________________________________
Dftot = df1 + df2
C. Describe in plain English:
"The observed difference between the means, 9.96, exceeds the critical value of the
difference between the means, 9.10. Therefore we reject the null hypothesis. Entirely
equivalently, the observed value of t, 2.20, exceeds the critical value of t, 2.013, so we
reject the null hypothesis. Because the results are statistically significant, we must
consider whether they are practically significant. The mean of the group taking the
drug (112.88) is .62 standard deviations higher than the mean of the other group
(102.92). That implies that approximately 73% of people taking the drug might be
expected to score higher than the average person not taking the drug."
```