HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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HLTH 300 Biostatistics for Public Health Practice,

Raul Cruz-Cano, Ph.D.2/3/2014 Spring 2014

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e

Chapter 2: Organizing the Data

1

2

2.1

WRT the homework: You are allowed to literally “copy” and “paste” the problem from the book

Announcement


Create frequency distributions of nominal data

Calculate proportions, percentages, ratios, and rates

Create simple and grouped frequency distributions

Create cross-tabulations

Distinguish between various forms of graphic presentations

CHAPTER OBJECTIVES

2.1

2.2

2.3

2.4

2.5

Create frequency distributions of nominal data

Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes

2.1

5

2.1

Formulas and statistical techniques are used by researchers to:

• Organize raw data• Test hypotheses

Raw data is often difficult to synthesize

Frequency tables make raw data easier to understand

Introduction

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2.1 Frequency Distributions of Nominal Data

Responses of Young Boys to Removal of Toy

Response of Child fCry 25Express Anger 15Withdraw 5Ply with another toy 5

N=50

Characteristics of a frequency distribution of nominal data:• Title• Consists of two columns:

• Left column: characteristics (e.g., Response of Child)

• Right column: frequency (f)

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2.1

Comparisons clarify results, add information, and allow for comparisons

Comparing Distributions

Response to Removal of Toy by Gender of Child

Gender of ChildResponse of Child Male FemaleCry 25 28Express Anger 15 3Withdraw 5 4Play with another toy 5 15 Total 50 50

Calculate proportions, percentages, ratios, and rates


2.2

9

2.2

Allows for a comparison of groups of different sizes

Proportion – number of casescompared to the total size of distribution

Percentage – the frequency of occurrence of a category per 100 cases

Proportions and Percentages

fPN

% (100) fN

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Examples



N=50

fPN

% (100) fN

Proportion of children that cried

5.5025

%505025100

Percentage of children that cried

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2.2

Ratio – compares the frequencyof one category to another

Rate – compares betweenactual and potential cases

Ratio and Rates

1

2

Ratioff

actual casesRate 1,000 potential casesff

12

Examples



N=50

Ratio of children that cried for every child that withdraw

5.525

children 1000per 50050251000

Rate of children that cried

1

2

Ratioff

actual casesRate 1,000 potential casesff

Create simple and grouped frequency distributions


2.3


2.3

Table 2.4


2.3

Table 2.5

Not in Order!

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2.3

Used to clarify the presentation of interval-level scores spread over a wide range

Class Intervals• Smaller categories or groups containing more than one score• Class interval size determined by the number of score values it

contains

Grouped Frequency Distribution of Interval Data

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2.3

Class Limits• The point halfway between

adjacent intervals • Upper and lower limits

– Distance from upper and lower limit determines the size of class interval

The Midpoint• The middlemost score value in a class interval

– The sum of the lowest and highest value in a class interval divided by two

Class Limits and the Midpoint

i U L

size of a class interval upper limit of a class interval lower limit of a class interval

iUL

lowest score value highest score value2

m

Careful, many time they are not as evident as they seem

18

More about the length of class intervals

f50-54 455-59 560-64 565-69 1270-74 1775-79 1280-84 785-89 490-94 295-95 3

71

TABLE 2.7 Grouped FrequencyDistribution of Final-ExaminationGrades for 71 Students

Usually the second category would be considered to be from 54.5 to 59.5

But notice that in a survey about age the respondents would consider to be from 55.0 to 55 + (364/365)

In other words “…comes down to personal preference, feasibility and logical sense, not what is strictly right or wrong” (page 52)

Midpoint = (55 +59)/2 = 114/2 =57

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2.3

Cumulative Frequencies• Total number of cases having a given score or a score that is

lower– Shown as cf– Obtained by the sum of frequencies in that category plus all

lower categories’ frequencies

Cumulative Percentage• Percentage of cases having a given score or a score that is

lower

Cumulative Distributions

% 100 cfcN


2.3

Table 2.7

f % cf c%50-54 4 5.63 4 5.6355-59 5 7.04 9 12.6860-64 5 7.04 14 19.7265-69 12 16.90 26 36.6270-74 17 23.94 43 60.5675-79 12 16.90 55 77.4680-84 7 9.86 62 87.3285-89 4 5.63 66 92.9690-94 2 2.82 68 95.7795-95 3 4.23 71 100.00

71 100.00

TABLE 2.7 Grouped FrequencyDistribution of Final-ExaminationGrades for 71 Students

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2.3

The percentage of cases falling at or below a given score

• Deciles – points that divide a distribution into 10 equally sized portions

• Quartiles – points that divide a distribution into quarters• Median – the point that divides a distribution in two, half above

it and half below it

Let’s talk about it after the Frequency Polygons and Line Charts

Percentiles

Create cross-tabulations


2.4


2.4

Table 2.17

Notice that sometimes is useful to divide the data using more than one variable, e.g. by Relationship and by Victim Sex

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2.4 Percents within Cross-Tabulations

Total Percents: % 100

Row Percents: % 100

Column Percents: % 100

total

row

column

ftotalNfrowN

fcolumnN

The choice comes down to which is more relevant to the purpose of the analysis

• If the independent variable is on the rows, use row percents• If the independent variable is on the columns, use column

percents• If the independent variable is unclear, use whichever percent is

most meaningful

25

26

Solution

a) Does you class determine if you buy a new car? Or Does buying a new car determines your class?

b) Pct. New Car = 100(17/ 73) = 23.28%c) Pct. Upper class with new car = 100(23/33) = 69.69%d) Pct. Middle class with new car = 100(6/27) = 22.22%e) Pct. Lower class with new car = 100(1/13) = 7.69%f) Effect of social class in buying a car?

No New Car New Car Total rowUpper Class 23 10 33Middle Class 21 6 27Lower Class 12 1 13Total Column 56 17 73

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Solution

Score Value f Class Interval f Midpoint Percentage cf Cum. Pct.

39 4 15-19 12 (15+19)/2 =17 100(12/74)=16.21 12 100(12/74)=16.21

38 4 20-24 23 (20+24)/2=22 100(23/74)=31.08 12+23=35 100(35/74)=47.29

35 2 25-29 22 (25+29)/2=27 100(22/74)=29.72 35+22=57 100(57/74)=77.02

32 3 30-34 7 (30+34)/2=32 100(7/74)=9.45 57+7=64 100(64/74)=86.48

31 4 35-39 10 (35+39)/2=37 100(10/74)=13.51 64+10=74 100

27 9 74 99.97=100 approx.

26 7

25 6

21 13

20 10

17 5

15 774

Distinguish between various forms of graphic presentations


2.5


2.5

Figure 2.4 Pie Charts


2.5

Figure 2.6 Bar Graph & Histograms


2.5

Figure 2.9 Frequency polygons

(frequency indicated at midpoint of each class)


Midpoint f % cf c%50-54 52.5 4 5.63 4 5.6355-59 57.5 5 7.04 9 12.6860-64 62.5 5 7.04 14 19.7265-69 67.5 12 16.9 26 36.6270-74 72.5 17 23.94 43 60.5675-79 77.5 12 16.9 55 77.4680-84 82.5 7 9.86 62 87.3285-89 87.5 4 5.63 66 92.9690-94 92.5 2 2.82 68 95.7795-95 97.5 3 4.23 71 100

71 100

From Table 2.7

52.5 57.5 62.5 67.5 72.5 77.5 82.5 87.5 92.5 97.50

10

20

30

40

50

60

70

80

90

100

50 percentile =70 approx

The smaller the class interval the better


2.5

Figure 2.11Taller than who? Flatter than who?


2.5

Figure 2.12


2.5

Figure 2.14 Line Chart(discrete values)


2.5

Figure 2.15 Maps

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Let’s work in MS Excel


Frequency distributions can be created to help researchers visualize distributions

Proportions, percentages, ratios, and rates can be calculated as a way to describe data

Simple frequency distributions can be created using data at any level of measurement, while interval level

data is needed to create a grouped frequency data

Cross-tabulations can be created to illustrate the relationship between two variables

CHAPTER SUMMARY

2.1

2.2

2.3

2.4

Several forms of graphs can be used to demonstrate patterns and relationships between variables 2.5

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2.3

Problems: 14 and 31I know that they are not exactly the same as those solved in class

No Excel this time, but maybe next

Homework

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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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