Post on 05-Feb-2016
description
Introduction to Using Statistical Analyses
Measures of Central Tendency(done . . .for now)
Measures of Variability Writing Using the Standard Normal Curve
A Reminder of the Way We Note Things:Our Shorthand
A Reminder of the Way We Note Things:Our Shorthand
A Reminder of the Way We Note Things:Our Shorthand
A Reminder of the Way We Note Things:Our Shorthand
A Reminder of the Way We Note Things:Our Shorthand
Population and Sample Means
Population and Sample Means
XXn
i
Introduction to Using Statistical Analyses
Measures of Central Tendency(done . . .for now)
Measures of Variability Writing Using the Standard Normal Curve
Assessing Dispersion by Looking at Spread
2
5
8
Data
Mean = 5
Assessing Dispersion by Looking at Spread
2
5
8
Data
Mean = 5
How far from the mean are the data?
Starting to Assess the Variance
2
5
8
- 5
- 5
- 5
= - 3
= 0
= 3
= - 3
= 0
= 3
A Formula to Assess the Variance
2
5
8
- 5
- 5
- 5
9
0
9
= - 3
= 0
= 3
A Formula to Assess the Variance
2
5
8
- 5
- 5
- 5
9
0
9= 18
= - 3
= 0
= 3
A Formula to Assess the Variance
2
5
8
- 5
- 5
- 5
9
0
9= 18
2 189
= - 3
= 0
= 3
A Formula to Assess the Variance
2
5
8
- 5
- 5
- 5
9
0
9= 18
2 189
THE VARIANCE
Sample and Population Standard Deviations
s
X X
ni
2
1
SAMPLE AND POPULATION TERMS
Sample Population
SAMPLE AND POPULATION TERMS
Sample Population
Mean
SAMPLE AND POPULATION TERMS
Sample Population
Mean
Variance
SAMPLE AND POPULATION TERMS
Sample Population
Mean
VarianceStandard Deviation
Introduction to Using Statistical Analyses
Measures of Central Tendency(done . . .for now)
Measures of VariabilityWriting Using the Standard Normal Curve
Introduction to Using Statistical Analyses
Measures of Central Tendency(done . . .for now)
Measures of Variability WritingUsing the Standard Normal
Curve
Standard Normal Curve
Standard Normal Curve
= 0
= 1- 3 + 3
z Scores when Data Do Not Already Have a Mean of 0 and a Standard Deviation of 1
z X
z Scores when Data Do Not Already Have a Mean of 0 and a Standard Deviation of 1
z X
z X Xs
or
Areas under the Standard Normal Curve
0
z = -1.67 z = 1
Areas under the Standard Normal Curve
0
z = -1.75 z = 1.75
Areas under the Standard Normal Curve
0
z = 1
Correlations
Correlation Example
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
Correlation Chart
Speaking Skill
Writing skill
0
1
2
3
4
5
6
7
0 1 2 3 4 5
* *
** *
Correlation Chart
Speaking Skill
Writing skill
0
1
2
3
4
5
6
7
0 1 2 3 4 5
* *
** *
Correlation Chart
Speaking Skill
Writing skill
0
1
2
3
4
5
6
7
0 1 2 3 4 5
* *
** *
Correlation Example Using z scores
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 1.27
- .63
0
.63
1.27
- 1.27
- .63
1.27
0
.63
Zx Zy
Correlation Example Using z scores
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 1.27
- .63
0
.63
1.27
- 1.27
- .63
1.27
0
.63
Zx Zy
1.61
.4
0
0
.8
Zx * Zy
Correlation Example Using z scores
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 1.27
- .63
0
.63
1.27
- 1.27
- .63
1.27
0
.63
Zx Zy
1.61
.4
0
0
.8
Zx * Zy
SUM = _ 2.81 __
n-1 = 4
Correlation Example Using z scores
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 1.27
- .63
0
.63
1.27
- 1.27
- .63
1.27
0
.63
Zx Zy
1.61
.4
0
0
.8
Zx * Zy
SUM = _ 2.81 __
n-1 = 4=.70
Correlation Example
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 2
- 1
0
1
2
- 2
- 1
2
0
1
X X Y Y
Correlation Example
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 2
- 1
0
1
2
- 2
- 1
2
0
1
X X Y Y X X Y Y* 4
1
0
0
2
Correlation Example
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 2
- 1
0
1
2
- 2
- 1
2
0
1
X X Y Y X X Y Y* 4
1
0
0
2 YYXX = 7
Correlation Example
1
2
3
4
5
3
4
7
5
6
Speaking Skill
X
Writing Skill
Y
- 2
- 1
0
1
2
- 2
- 1
2
0
1
X X Y Y X X Y Y* 4
1
0
0
2 YYXX = 7
n-1 = 4
rs sX Y
7
41 75.
*
Correlation Computation
rs sX Y
7
41 75.
*
Correlation Computation
rs sX Y
7
41 75.
*
Correlation Computation
rs sX Y
7
41 75.
*
r
r
1 751 58 1 581 752 5
70
.. * ...
.
Correlation Computation
rs sX Y
7
41 75.
*
r
r
1 751 58 1 581 752 5
70
.. * ...
.
Correlation Computation