**The first function.**

**Descriptive Statistics**

Frequency Distributions

Simple Frequency Distributions

for Ordinal and Interval data

Regular Frequency Distribution

Complex Frequency Distributions

Cross-tabulations

**Graphic Representations**

**Pie Chart**

**Kurtosis and Skewness**

Nominal Data Frequency Distributions contain two columns

characteristic (labeled category) being presented

attribute

the frequency that is observed (f)

Occupation

f

Police Officer

Nurse

Lawyer

Mechanic

Salesperson

Computer Tech

Teacher

Other

Not Applicable

38

20

4

14

24

6

16

34

44

n= 200

Occupation

f

Police Officer

Nurse

Lawyer

Mechanic

Salesperson

Computer Tech

Teacher

Other

Not Applicable

38

20

4

14

24

6

16

34

44

n= 200

More Descriptive Statistics for Nominal Data

P

.19

.10

.02

.07

.12

.03

.08

.17

.22

%

1.0

19

10

2

7

12

3

8

17

22

100

Proportions and Percentages

further clarify existing data

used to make comparisons between groups of unequal size

standardization

Proportion compares the number of cases within a given category (f) with the total size of the distribution (n)

Percentage indicates relative size of category per 100 cases

P = f/n

% = (100)f/n

Grouped Frequency Distribution

Cumulative Frequency Distribution

Frequency distribution of attitudes toward support of Sex Registration Laws

Strongly favor

Somewhat favor

Slightly favor

Slightly unfavor

Somewhat unfavor

Strongly unfavor

8

5

3

3

5

6

n = 30

Strongly favor

Slightly unfavor

Slightly favor

Somewhat unfavor

Strongly unfavor

Somewhat favor

8

3

3

5

6

5

n = 30

arrange cases in an order that reflects the degree to which a particular characteristic is present

distribution should take the rank into account

condense separate scores into a number of smaller categories or groups

99

98

97

96

95

94

93

92

91

90

89

88

87

86

85

84

83

82

81

80

79

78

77

76

75

74

73

72

71

70

69

68

67

66

65

64

63

62

61

60

59

58

57

56

55

54

53

52

51

50

0

1

0

1

1

0

0

1

1

0

1

0

1

0

2

1

0

3

1

2

8

1

0

2

1

1

1

2

4

9

3

5

1

3

0

1

2

0

0

2

3

1

0

1

0

1

0

1

1

1

Grade

Grade

Grade

Grade

Grade

f

f

f

f

f

Class Interval

f

%

"class intervals"

n=71

95-99

90-94

85-89

80-84

75-79

70-74

65-69

60-64

55-59

50-54

3

2

4

7

12

17

12

5

5

4

4.23

2.82

5.63

9.86

16.90

23.94

16.90

7.04

7.04

5.63

n=71

100

Class Interval

f

%

95-99

90-94

85-89

80-84

75-79

70-74

65-69

60-64

55-59

50-54

3

2

4

7

12

17

12

5

5

4

4.23

2.82

5.63

9.86

16.90

23.94

16.90

7.04

7.04

5.63

n=71

100

cf

c%

71

68

66

62

55

43

26

14

9

4

100.00

95.76

92.94

87.31

77.45

60.55

36.61

19.71

12.67

5.63

cumulative frequency (cf) is the total number of cases having any given score

OR

a score that is lower

cumulative percent (c%) is the percentage of cases having any given score

OR

a score that is lower

Guidelines for constructing class intervals

2. Use 8 to 15 intervals

3. Use an interval size of 2, 3, 5 or a multiple of 5, selecting the smallest size that satisfies guideline 2

4. Make the lowest score in the interval a multiple of the interval size

5. Use the same widths with no gaps or overlaps

Flexible Class Intervals

every once in a while, there will be a data that requires an "open-ended" class interval

Only use these for the lowest or highest interval

a table that presents the distribution (frequencies and percents) of one variable, usually the dependent variable, across the categories of one or more variables.

use percentages to make meaningful comparisons

percentages calculated based on row and column totals

use independent variable to determine percentage

1. Use whole numbers

Feelings about pornography laws

Total

Illegal to All

Illegal under 18

Legal

Total

372

596

36

1004

Feelings about pornography laws x Gender

Total

Illegal to All

Illegal under 18

Legal

Total

372

596

36

1004

Male

Gender

Female

112

322

22

456

260

274

14

548

Feelings about pornography laws x Gender

Total

Illegal to All

Illegal under 18

Legal

Total

372

596

36

1004

Male

Gender

Female

112

322

22

456

260

274

14

548

24.6%

47.4%

37.1%

70.6%

4.8%

50.0%

59.4%

2.6%

3.6%

100%

100%

100%

useful for only a few categories (nominal data)

**Bar Chart**

**Histogram**

nominal and ordinal

interval and ratio

emphasizes differences

emphasizes continuity

**Frequency Polygon**

continuity at the case-level

Platykurtic is flat

Mesokurtic is "relatively normal"

Leptokurtic is peaked and tall

Negatively skewed - the "tail" runs to the left

Positively skewed - the "tail" runs to the right

Symmetrical - identical tails (mirror image)

does it make sense?

**End**