Introduction to Using Statistical Analyses u Measures of Central Tendency (done...for now) u Measures of Variability u Writing u Using the Standard.

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





Population and Sample Means

Population and Sample Means

XX

ni



(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


2

5

8

- 5

- 5

- 5

9

0

9= 18

= - 3

= 0

= 3


2

5

8

- 5

- 5

- 5

9

0

9= 18

2 189

2 189

= - 3

= 0

= 3


2

5

8

- 5

- 5

- 5

9

0

9= 18

2 189

2 189

THE VARIANCE

Sample and Population Standard Deviations

s

X X

n

i

2

1

SAMPLE AND POPULATION TERMS

Sample Population


Sample Population

Mean


Sample Population

Mean

Variance


Sample Population

Mean

Variance

Standard Deviation



(done . . .for now) Measures of Variability

Writing Using the Standard Normal Curve


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

zX

z Scores when Data Do Not Already Have a Mean of 0 and a Standard Deviation of 1

zX

zX X

s

or

Areas under the Standard Normal Curve

0

z = -1.67 z = 1


0

z = -1.75 z = 1.75


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


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


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


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.

*


rs sX Y

7

41 75.

*


rs sX Y

7

41 75.

*

r

r

1 75

1 58 1 581 75

2 570

.

. * .

.

..


rs sX Y

7

41 75.

*

r

r

1 75

1 58 1 581 75

2 570

.

. * .

.

..


Introduction to Using Statistical Analyses u Measures of Central Tendency (done...for now) u Measures of Variability u Writing u Using the Standard.

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