Statistics

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# Statistics - PowerPoint PPT Presentation

Statistics. Descriptive Statistics Inferential Statistics. Descriptive statistics Used to describe a set of data Inferential statistics Used to draw inferences about a population based on data obtained from a sample. Parameter Statistic. Scales of Measurement.

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Descriptive Statistics

Inferential Statistics

Descriptive statistics

Used to describe a set of data

Inferential statistics

Used to draw inferences about a population based on data obtained from a sample.

Parameter

Statistic

Scales of Measurement

Nominal scales (Categorical data)

Ordinal scales

Interval scales

Ratio scales

Distributions

IQ Scores

113, 117, 84, 103, 105, 108, 115, 126, 103, 112, 106, 111, 113, 90, 107, 76, 109, 97, 103, 97, 89, 101, 93, 99, 115, 94, 94, 94, 108, 97, 95, 87, 107, 97, 88, 99, 97, 82, 112, 91, 107, 93, 83, 99, 100, 92, 102, 93, 100, 83, 125, 96, 84, 113, 113, 96, 97, 88, 100, 95, 86, 77, 80, 125, 110, 114, 121, 102, 90, 103, 91, 103, 109, 104, 79, 100, 85, 76, 115, 105, 95, 88, 93, 111, 107, 108, 98, 84, 123, 107, 118, 93, 101, 92, 99, 92, 136, 121, 97, 101, 102, 114, 103, 81, 71, 104, 85, 106, 120, 108, 112, 131, 94, 104, 121, 123, 91, 103, 93, 102

N = 120

IQ Scores - Ranked

71, 76, 76, 77, 79, 80, 81, 82, 83, 83, 84, 84, 84, 85, 85, 86, 87, 88, 88, 88, 89, 90, 90, 91, 91, 91, 92, 92, 92, 93, 93, 93, 93, 93, 93, 94, 94, 94, 94, 95, 95, 95, 96, 96, 97, 97, 97, 97, 97, 97, 97, 98, 99, 99, 99, 99, 100, 100, 100, 100, 101, 101, 101, 102, 102, 102, 102, 103, 103, 103, 103, 103, 103, 103, 104, 104, 104, 105, 105, 106, 106, 107, 107, 107, 107, 107, 108, 108, 108, 108, 109, 109, 110, 111, 111, 112, 112, 112, 113, 113, 113, 113, 114, 114, 115, 115, 115, 117, 118, 120, 121, 121, 121, 123, 123, 125, 125, 126, 131, 136

N = 120

Frequency distribution of IQ scores

Cumulative

Value

Frequency

Percent

Percent

71

.8

1

.8

76

2

1.7

2.5

77

1

.8

3.3

79

.8

1

4.2

80

.8

5.0

1

81

1

.8

5.8

82

1

.8

6.7

83

1.7

2

8.3

84

3

2.5

10.8

85

2

1.7

12.5

86

1

.8

13.3

87

1

.8

14.2

88

3

2.5

16.7

89

1

.8

17.5

90

2

1.7

19.2

91

3

2.5

21.7

.

.

.

.

136

1

.8

100.0

Total

120

100

Grouped Frequency Distribution of IQ scores

Mid-

Cumulative

Value

F

Percent

point

Percent

72

1

.8

.8

70 - 74

4

3

.3

4

75 -79

77

.2

82

8

6

.6

10

.8

80 - 84

8

6

.6

85 - 89

87

17

.5

92

18

15

.0

32

.5

90 - 95

95 - 99

97

17

14

.2

46

.7

102

21

17

.5

64

.2

100 -104

107

15

12

.5

76

.7

105 - 109

12

10

.0

86

.7

110 - 114

112

117

5

4

.2

90

.8

115 - 119

6

5

.0

95

.8

120 - 124

122

127

3

2

.5

98

.3

125 - 129

1

.8

.2

130 - 134

132

99

137

1

.8

100

.0

135 - 139

N

120

Measures of Central Tendency

Mode

The most common score

Grouped Frequency Distribution of IQ scores

Mid-

Cumulative

Value

F

Percent

point

Percent

70 - 74

72

1

.8

.8

77

4

3

.3

4

.2

75 -79

8

6

.6

80 - 84

82

10

.8

8

6

.6

85 - 89

87

17

.5

92

18

15

.0

32

.5

90 - 95

97

17

14

.2

46

.7

95 - 99

102

21

17

.5

64

.2

100 -104

107

15

12

.5

76

.7

105 - 109

112

12

10

.0

86

.7

110 - 114

117

5

4

.2

90

.8

115 - 119

122

6

5

.0

95

.8

120 - 124

127

3

2

.5

98

.3

125 - 129

132

1

.8

99

.2

130 - 134

1

.8

.0

137

100

135 - 139

N

120

Measures of Central Tendency

Median (Mdn)

The score that corresponds to the point at or below which 50% of the scores fall. (The 50th percentile.)

Sample A:26811141620

Mdn = 11.0

Sample B:2681114162051

Mdn = 12.5

2

N

+

1

Median location =

Grouped Frequency Distribution of IQ scores

Mid-

Cumulative

Value

F

Percent

point

Percent

72

1

.8

.8

70 - 74

4

3

.3

4

75 -79

77

.2

82

8

6

.6

10

.8

80 - 84

8

6

.6

85 - 89

87

17

.5

92

18

15

.0

32

.5

90 - 95

95 - 99

97

17

14

.2

46

.7

102

21

17

.5

64

.2

100 -104

107

15

12

.5

76

.7

105 - 109

12

10

.0

86

.7

110 - 114

112

117

5

4

.2

90

.8

115 - 119

6

5

.0

95

.8

120 - 124

122

127

3

2

.5

98

.3

125 - 129

1

.8

.2

130 - 134

132

99

137

1

.8

100

.0

135 - 139

N

120

Mean ( 0, :or M)

The average score

å

X

( 3 = capital Sigma = add up all the numbers)

X

=

N

Sample A: 2 6 8 11 14 16 20

77

X

=

=

11

.

0

(Mdn= 11.0 )

A

7

Sample B 2 6 8 11 14 16 20 51

128

( Mdn = 12.5 )

X

=

=

16

B

8

Outlier

Properties of the mean

0

0

X

X -

X -

2

2 - 11

-9

6

-4

6 - 11

8

8 - 11

-3

11

0

11 - 11

14

3

14 - 11

16

4

16 - 11

9

9

20

20 - 11

0

0

\'

\'

X -

X -

= 0

= 0

Scores

10

12

15

18

20

Sample A

2

8

15

22

28

Sample B

15

15

15

15

15

Sample C

M

Scores

Mdn

10

12

15

18

20

15

15

Sample A

2

8

15

22

28

15

15

Sample B

15

15

15

15

15

15

15

Sample C

Measures of Variability

Range

The scale distance between the largest and the smallest scores.

Scores

Mdn

M

12

15

18

20

15

15

Sample A

10

2

8

15

22

28

15

15

Sample B

15

15

15

15

15

15

15

Sample C

RangeA = 20 - 10 = 10

RangeB = 28 - 2 = 26

RangeC = 15 - 15 = 0

Interquartile Range

Is the distance between the score occuring at the 25th percentile and the score occuring at the 75th percentile.

Mean (Average) Deviation

å

(

X

-

X

)

N

0

0

X

X -

X -

2

2 - 11

-9

6

-4

6 - 11

8

-3

8 - 11

11

0

11 - 11

14

3

14 - 11

16

4

16 - 11

20

20 - 11

9

9

0

0

\'

\'

X -

X -

= 0

= 0

Mean Absolute Deviation

å

X

-

X

N

0

0

X

X -

*

X -

*

2

2 - 11

9

6

6 - 11

5

8

8 - 11

3

11

11 - 11

0

14

14 - 11

3

16

16 - 11

4

20

20 - 11

9

9

0

0

\'

\'

X -

X -

= 32

= 32

Variance (for population)

å

2

(

X

-

X

)

2

s

=

N

0

0

X

Sample

2

)

X -

(X -

A

-5

10

25

12

-3

9

0

0

15

18

3

9

20

5

25

G

0

=

65

68

0

15

=

å

2

(

X

-

X

)

68

2

s

=

=

=

13

.

60

N

5

Standard Deviation (for population)

å

2

(

X

-

X

)

s

=

N

0

0

X

Sample

2

)

X -

(X -

A

10

-5

25

12

-3

9

0

0

15

18

3

9

5

20

25

G

65

0

68

=

0

15

=

å

2

(

X

-

X

)

68

s

=

=

=

13

.

6

=

3

.

69

N

5

Variance (for sample)

å

2

(

X

-

X

)

2

s

=

N

-

1

0

0

X

Sample

2

)

X -

(X -

A

10

-5

25

12

-3

9

15

0

0

3

9

18

20

5

25

G

=

65

0

68

0

15

=

å

2

(

X

-

X

)

68

2

s

=

=

=

17

.

00

N

-

1

4

Standard Deviation (for sample)

å

2

(

X

-

X

)

s

=

N

-

1

0

0

X

Sample

2

)

X -

(X -

A

10

-5

25

12

-3

9

15

0

0

3

9

18

5

20

25

G

=

65

0

68

0

15

=

å

2

(

X

-

X

)

68

s

=

=

=

17

.

0

=

4

.

12

N

-

1

4