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# Statistics Lecture 2

CJ3347-256 Spring 2013
by

## Dustin Melbardis

on 4 February 2015

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#### Transcript of Statistics Lecture 2

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
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
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
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