Degrees of freedom
Calc t-test
Calc Dispersion
Formulas
SSregression = SStotal * rsquared
SSerror = SStotal * (1- rsquared)
SStotal = SSy
df(regression) = k – 1
df(error) = N – k
df(total) = N-1
F = mean squares regression divided by means squares error
Formula for Central Tendency
MEAN.
You probably already know this formula. A mean is the average of scores. We like to use it becuase we don’t have to arrange the scores in any particular order before calculating it. We just add up all the numbers and divide by the number of scores. In statistical vocab we “sum” the numbers and divided the sum by N (the number of scores).
∑X/N
MEDIAN
A median requires that we put the numbers in order (from high to low, or low to high). The median is the score in the middle (if there are an odd number of scores) or the average of the two middle-most scores (if there are an even number of scores). That too much work, so we prefer the mean.
There is no easy formula for median.
MODE
The mode is the most popular score (most common). If you plot a distribution, the mode will be the highest spot on the distribution. It will be the top of the mountain. If your mountain has more than one peak, the distribution will be bimodal (2 high spots) or multimodal (several high spots).
There is no easy formula for mode.
Practice z Scores
Item 1
Calculate the z-score, assuming:
X = 10
mean = 50
stdev = 10
z score _____
Item 2
Calculate the z-score, assuming:
X = 80
mean = 50
stdev = 15
X – mean _____
z score _____
Item 3
Calculate the z-score, assuming:
X = 112
mean = 100
stdev = 15
X – mean _____
z score _____
Item 4
Calculate the raw score, assuming:
z = 1.5
mean = 115
stdev = 10
z * stdev _____
X _____
Item 5
Calculate the raw score, assuming:
z = -1.37
mean = 100
stdev = 20
z * stdev _____
X _____
Item 6
Calculate the raw score, assuming:
z = -1.37
mean = 100
stdev = 20
X _____
ANSWERS
Item 1
Calculate the z-score, assuming:
X = 10
mean = 50
stdev = 10
X – mean = – 40
z score = – 4.
Item 2
Calculate the z-score, assuming:
X = 80
mean = 50
stdev = 15
X – mean = 30
z score = 2.0
Item 3
Calculate the z-score, assuming:
X = 112
mean = 100
stdev = 15
X – mean = 12
z score = .80
Item 4
Calculate the raw score, assuming:
z = 1.5
mean = 115
stdev = 10
z * stdev = 15
X = 130
Item 5
Calculate the raw score, assuming:
z = -1.37
mean = 100
stdev = 20
z * stdev = 27.4
X = 72.6
Item 6
Calculate the raw score, assuming:
z = 2.54
mean = 80
stdev = 20
X = 130.8
2.54*20 = 50.8
50.8 + 80 = 130.8
Practice t Tests
Independent Student t
Item #1
Calculate am independent t-test for the following data:
X1 X2
6 12
4 4
2 7
3 10
9 5
6 8
5 3
Mean of group 1 _____
Mean of group 2 _____
Difference between the means _____
SS of group 1 _____
SS of group 2 _____
n(n-1) _____
t = _____
How many degrees of freedom (df) at in this study_____
What is the critical value for t (2 tailed, .05 alpha) _____
Is the t significant _____
Item #2
Calculate am independent t-test for the following data:
X1 X2
15 3
11 5
8 4
12 2
7 6
Mean of group 1 _____
Mean of group 2 _____
SS of X1 _____
SS of X2 _____
t = _____
Item #3
Calculate am independen t-test for the following data:
X1 X2
6 3
7 5
6 3
8 2
4 7
11 4
t = _____
How many degrees of freedom (df) at in this study ____
What is the critical value for t (2 tailed, .05 alpha) _____
Is the t significant? _____
Item #4
Which students do significantly better in reading (Words per minute):
High Sch College
7 5
4 3
6 1
6 11
3 8
2 8
1 13
6 9
t =
.
Item #5
Which cars are the safest (accidents):
Foreign Domestic
16 1
14 3
12 9
18 11
12 6
7 1
t =
Item #6
Which dogs are the meanest (bites per minute):
Big Little
1 6
4 3
3 9
8 11
2 16
7 11
5 22
3 7
t =
ANSWERS
Item #1
Calculate am independent t-test for the following data:
X1 X2
6 12
4 4
2 7
3 10
9 5
6 8
5 3
Mean of group 1 5
Mean of group 2 7
Difference between the means 2
SS of group 1 32
SS of group 2 64
n(n-1) 42
t = 1.32
How many degrees of freedom (df) at in this study N-2 = 12
What is the critical value for t (2 tailed, .05 alpha) 2.18
Is the t significant No. The calculated value (1.32) is not equal to (or bigger) that the critical value (2.18). The differences between the groups is likely to be due to chance.
Item #2
Calculate am independent t-test for the following data:
X1 X2
15 3
11 5
8 4
12 2
7 6
Mean of group 1 10.60
Mean of group 2 4.00
SS of X1 41.20
SS of X2 10
t = 4.13
Item #3
Calculate am independen t-test for the following data:
X1 X2
6 3
7 5
6 3
8 2
4 7
11 4
t = 2.48
How many degrees of freedom (df) at in this study 10
What is the critical value for t (2 tailed, .05 alpha) 2.23
Is the t significant? Yes
Item #4
Which students do significantly better in reading (Words per minute):
High Sch College
7 5
4 3
6 1
6 11
3 8
2 8
1 13
6 9
7 5
4 3
6 1
6 11
3 8
2 8
1 13
6 9
t = 1.77
Which students do significantly better in reading:
Item #5
Which cars are the safest (accidents):
Foreign Domestic
16 1
14 3
12 9
18 11
12 6
7 1
16 1
14 3
12 9
18 11
12 6
7 1
t = 3.45
Which cars are the safest (accidents):
Item #6
Which dogs are the meanest (bites per minute):
Big Little
1 6
4 3
3 9
8 11
2 16
7 11
5 22
3 7
1 6
4 3
3 9
8 11
2 16
7 11
5 22
3 7
t = 2.37
Which dogs are the meanest (bites per minute):
