• Study Resource
• Explore

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

History of statistics wikipedia, lookup

Student's t-test wikipedia, lookup

Taylor's law wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Resampling (statistics) wikipedia, lookup

Misuse of statistics wikipedia, lookup

Degrees of freedom (statistics) wikipedia, lookup

Psychometrics wikipedia, lookup

Sufficient statistic wikipedia, lookup

Transcript
```Comparing Two Groups
Statistics 2126
So far..
• We have been able to compare a sample
mean to a population mean
– z test
– t test
• Often times though we have two groups to
compare
• Is Group 1 different from Group 2
Matched pairs or correlated t test
• AKA dependent sample t test
• When subjects are matched on a variable
or are used as their own controls, a sort of
before and after thing if you will
• Be very careful with this
• But it is way powerful and easy to do
Back to our mythical IQ course..
Before
After
Difference
103
98
-5
100
107
7
111
119
8
97
100
3
133
134
1
106
111
5
87
85
-2
A couple of summary statistics
 d  27
d

d 
n
27
d 
7
d  3.86
sd  3.48
Now it is a simple t test
d 
t
sd / n
3.86  0
t
3.48 / 7
3.86
t
3.48 / 2.65
3.86
t
1.31
t  2.95
And now for the decision
•
•
•
•
t(6) = 2.447
tobt = 2.95
Reject H0
Our IQ course works!!
Two sample problems
• While is is useful to know how to compare
a sample mean to a population mean and
check for significance it is not all that
common
• We rarely know μ
– Sometimes we do
• IQ
• Differences
• Theoretical values
The much more common question
is…
• Does one group differ from another?
• Let’s say we had two classes with different
teaching methods
• Is there an effect of teaching method?
Statistic
Class 1
Class 2
Mean
77
71
Standard
deviation
6.2
6.7
Number of
students
49
52
Our hypotheses
•
•
•
•
•
•
Are the two classes different?
H 0 μ1 = μ2
H A μ1 ≠ μ2
Or we could restate them like this:
H 0 μ1 - μ2 = 0
H A μ1 ≠ μ2 ≠ 0
Let’s go back to the original t
formula
Statistic
H0
↓
↓
x
t
s/ n
← Error
Figure it out
( x1  x2 )  ( 1   2 )
t
error
practicall y....
( x1  x2 )
t
error
the values of s for
each group
• They must be
weighted
2
1
2
2
s
s

n1 n2
6.2
2
49

6.7
2
52
So the formula is
t
x1  x2
2
1
2
2
s
s

n1 n1
Degrees of freedom
• With a one sample t test we lose one
degree of freedom
• Because we calculated one standard
deviation
• Here was have calculated 2
• So we lose 2 df
• In our case we have 99 df
Sub in the values
t
77  71
2
2
6.2 6.7

49
52
6
t
1.65
t  4.67
rejectH0
conclusions
• All t tests are based on the same formula
• Keep the assumptions in mind
– SRS
– Homogeneity of variance
– Independence of observations
```
Related documents