Another Information-Gathering Technique & Introduction to Quantitative Data Analysis

Another Information-Gathering Technique & Introduction to Quantitative Data Analysis

Neuman and Robson Chapter 11.

Research Data library at SFUhttp://www.sfu.ca/rdl/

Quiz 2 Coverage• New Material from the Lectures and from the following

Chapters – 7 (Sampling), 8 (Surveys), 10 (Nonreactive Measures &

Existing Statistics) and the beginning of Chapter 11 (univariate statistics)

• The quiz may also include material covered in the first quiz especially: – Standardization & rates– Scales & indices– validity & reliability, – levels of measurement, – the notions of exhaustive & mutually exclusive categories.

Types of Equivalence for comparative research using existing statistics

Types of Equivalence for comparative research using existing statistics

• lexicon equivalence (technique of back translation)

• contextual equivalence (ex. role of religious leaders in different societies)

• conceptual equivalence (ex. income)• measurement equivlence (ex. different

measure for same context)

Ethical Issues in Comparative ResearchEthical Issues in Comparative Research

• ethical issues sometimes very important – ex. impact of demographic research on funding of

developing countries, controversy surrounding studies of the origins of AIDS

• sensitivity, privacy etc.sometimes still issues even if “subjects” dead.

Quantitative Data

• Types of Statistics– Descriptive– Inferential

• Common Ways of Presenting Statistics– Tables– Charts– Graphs

Data Preparation

• Recall: Coding Issues with War & Peace Journalism codes last day

• Entering Data into Spreadsheet or data processing software

• Cleaning Data

Recall: Coding Principles

• categories– exhaustive– mutually exclusive

• consistent for all cases• comparable with other studies

Ways of Developing Coding Categories

• pre-defined coding schemes–e.g. close-ended questions– Ex. Coding Missing Values (conventions not

always used)• not applicable=77, • don’t know=88,• no response=99

• post-collection analysis

More Examples of Coding Process

• Sheet for One Television Commercial• Excel spreadsheet showing entered codes• SPSS example

Data entry conventions

Discrete & Continuous Variables

• Continuous– Variable can take infinite (or large) number of values

within range• Ex. Age measured by exact date of birth

• Discrete– Attributes of variable that are distinct but not

necessarily continuous• Ex. Age measured by age groups (Note: techniques exist

for making assumptions about discrete variables in order to use techniques developed for continuous variables)

Cleaning Data

• checking accuracy & removing errors –Possible Code Cleaning• check for impossible codes (errors)

– Some software checks at data entry– Examine distributions to look for impossible codes

– Contingency cleaning• inconsistencies between answers (impossible

logical combinations, illogical responses to skip or contingency questions)

Descriptive Statistics (some topics for next few weeks)

• Univariate (one variable)– Frequency distributions– Graphs & charts– Measures of central tendency– Measures of dispersion

• Bivariate (two variables)– Crosstabulations– Scattergrams & other types of graphs– Measures of association

• Multivariate (more than two variables)– Statistical control– Partials– Elaboration paradigm

Frequency Distribution (Univariate)Table 5-1 Alienation of Workers__________________________________---------------------------------------------------------Level of Alienation Frequency---------------------------------------------------------High 20Medium 67Low 13 (Sub Total) 100

(N=150)No Response 60

(Total) (N=210)

Simple Univariate Frequency Distributions and Percentages

• univariate:= one variable• “raw count” (frequencies, percentages)

Conventions in table design

• total number of cases (N=)• grouping cases – pro: see patterns– con: lose information

Graph of Frequency Distribution (Univariate)

Another visual representation of a distributions: Pie charts

Critically Analyzing Data on Frequency Distributions: Collapsing Categories and Treatment of Missing Data

• Consider Raw Data (Numbers) not just percentages

• Examine data preparation – Treatment of

missing cases?– Collapsing

categories?

Johnson, A. G. (1977). Social Statistics Without Tears. Toronto: McGraw Hill.

Treatment of Missing Data: Raw Data

Table 5-1 Alienation of Workers__________________________________---------------------------------------------------------Level of Alienation Frequency---------------------------------------------------------High 20Medium 67Low 13 (Sub Total) 100

(N=150)No Response 60

(Total) (N=210)

Treatment of Missing Data (%)• Comparison of % distributions and without

non respondents

Table 5-1 Alienation of Workers

Level of Alienation F %High 30 14 Medium 100 48 Low 20 10 No Response 60 29

(Total) 210 100

Table 5-1 Alienation of Workers

Level of Alienation F %High 30 20 Medium 100 67 Low 20 13

(Total) 150 100

Treatment of Missing Data (%)• Comparison with high & medium collapsed

Table 5-1 Alienation of Workers

Level of Alienation F %High & Medium 130 62 Low 20 10 No Response 60 29

(Total) 210 100

Table 5-1 Alienation of Workers

Level of Alienation F %High & Medium 130 87 Low 20 13

(Total) 150 100

Non-respondents included Non-respondents eliminated

Treatment of Missing Data (%)• Comparison with medium & low collapsed

Table 5-1 Alienation of Workers

Level of Alienation F %High 30 14 Medium & Low 120 58 No Response 60 29

(Total) 210 100

Table 5-1 Alienation of Workers

Level of Alienation F %High 30 20 Medium & Low 120 80

(Total) 150 100

Non-respondents included Non-respondents eliminated

Grouping Response Categories(%)

• Comparison of with high & medium response categories collapsed

Table 5-1 Alienation of Workers

Level of Alienation Freq % High& medium 87Low 13

(Total) 150

Table 5-1 Alienation of Workers

Level of Alienation Freq %High & Medium 62Low 10No Response 29

(Total) 210 100

Core Notions in Basic Univariate Statistics

Ways of describing data about one variable (“uni”=one)–Measures of central tendency• Summarize information about one variable • three types of “averages”: arithmetic mean,

median, mode

–Measures of dispersion• Analyze Variations or “spread”• Range, standard deviation, percentiles, z-scores

Mode

Babbie (1995: 378)

• most common or frequently occurring category or value (for all types of data)

Graph (Normal Distribution) with single mode

Bimodal Distribution

• When there are two “most common” values that are almost the same (or the same)

Median

Babbie (1995: 378)

• middle point of rank-ordered list of all values (only for ordinal, interval or ratio data)

Mean (arithmetic mean)

Babbie (1995: 378)

– Arithmetic “average” = sum of values divided by number of cases (only for ratio and interval data)

Two Data Sets with the Same Mean

Normal Distribution & Measures of Central Tendency

Neuman (2000: 319)Neuman (2000: 319)

• Symmetric• Also called the “Bell Curve”

Skewed Distributions & Measures of Central Tendency

Neuman (2000: 319)Neuman (2000: 319)

Skewed to the left

Skewed to the right

Normal & Skewed Distributions

Why Measures of Central Tendency are not enough to describe distributions:

Crowd Example

Why Measures of Central Tendency are not enough to describe distributions:

Crowd Example

• 7 people at bus stop in front of bar aged 25,26,27,30,33,34,35– median= 30, mean= 30

• 7 people in front of ice-cream parlour aged 5,10,20,30,40,50,55– median= 30, mean= 30

• BUT issue of “spread” socially significant

Measures of Variation or Dispersion Measures of Variation or Dispersion

• range: distance between largest and smallest scores

• standard deviation: for comparing distributions • percentiles: for understanding position in

distribution% up to and including the number (from below)

• z-scores: for comparing individual scores taking into account the context of different distributions

Range & Interquartile range

• distance between largest and smallest scores– what does a short distance between the scores tell us

about the sample?– problems of “outliers” or extreme values may occur

Interquartile range (IQR) • distance between the 75th percentile and the 25th

percentile• range of the middle 50% (approximately) of the data• Eliminates problem of outliers or extreme values

• Example from StatCan website (11 in sample) – Data set: 6, 47, 49, 15, 43, 41, 7, 39, 43, 41, 36 – Ordered data set:6, 7, 15, 36, 39, 41, 41, 43, 43, 47, 49– Median:41 – Upper quartile: 41– Lower quartile: 15 – IQR= 41-15

Standard Deviation and Variance

• Inter quartile range eliminates problem of outliers BUT eliminates half the data

• Solution? measure variability from the center of the distribution.

• standard deviation & variance measure how far on average scores deviate or differ from the mean.

Calculation of Standard Deviation

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Neuman (2000: 321)Neuman (2000: 321)

Calculation of Standard Deviation

Neuman (2000: 321)Neuman (2000: 321)

Standard Deviation Formula

Neuman (2000: 321)Neuman (2000: 321)

Calculation of Standard Deviation

Neuman (2000: 321)Neuman (2000: 321)

Interpreting Standard Deviation

• amount of variation from mean• social meaning depends on exact case

Details on the Calculation of Standard Deviation

Neuman (2000: 321)Neuman (2000: 321)

The Bell Curve & standard deviation

Discussion of Preceding Diagram

• “Many biological, psychological and social phenomena occur in the population in the distribution we call the bell curve (Portney & Watkins, 2000).” link to source

• Preceding picture – a symmetrical bell curve, – average score [i.e., the mean] in the middle, where the ‘bell’

shape tallest. – Most of the people [i.e., 68% of them, or 34% + 34%] have

performance within 1 segment [i.e., a standard deviation] of the average score.”

Interpreting Standard Deviation• amount of variation

from mean• Illustration: high &

low standard deviation

• meaning depends on exact case

Another Diagram of Normal Curve (Showing Ideal Random Sampling Distribution, Standard

Deviation & Z-scores)

Example:Central Tendency & Dispersion (description of

distributions)

Example:Central Tendency & Dispersion (description of

distributions)Recall:• 7 people at bus stop in front of bar aged

25,26,27,30,33,34,35– median= 30, mean= 30– Range= 10, standard deviation=10.5

• 7 people in front of ice-cream parlour aged 5,10,20,30,40,50,55– median= 30, mean= 30– Range= 50, standard deviation=17.9

Other ways of characterizing dispersion or spread

Techniques for understanding position of a case (or group of cases) in the context all of cases

• Percentiles• Standard Scores– z-scores

Percentile• 1st Calculate rank then choose a rank (score) and figure

out percentage equal to or less than the rank (score)– Link to more complex definition of percentile

• % up to and including the number (from below)– “A percentile rank is typically defined as the proportion of

scores in a distribution that a specific score is greater than or equal to. For instance, if you received a score of 95 on a math test and this score was greater than or equal to the scores of 88% of the students taking the test, then your percentile rank would be 88. You would be in the 88th percentile”

• Also used in other ways (for example to eliminate cases)

Normal Distribution with Percentiles

z-scores

• For understanding how a score is positioned in the data set

• to enable comparisons with other scores from other data sets– (comparing individual scores in different distributions)• example of two students from different schools with

different GPAs

– comparing sample distributions to population. How representative is sample to population under study?

Calculating Z-Scores

• z-score=(score – sample mean)/standard deviation of set– Link to formula– Link to z-score calculator

Calculating Z-Scores

Using Z-scores to compare two students’ from different schools

• Susan has GPA of 3.62 & Jorge has GPA of 3.64• Susan from College A– Susan’s Grade Point Average =3.62– Mean GPA= 2.62– SD= .50– Susan’s z-score= 3.62-2.62=1.00/.50=2– Susan’s grade is two Standard deviations above mean

at her school

Using Z-scores to compare two students’ from different schools (continued)

• Jorge from College B– Jorge’s GPA =3.64– Mean GPA= 3.24– SD=.40– Jorge’s z-score= 3.64-3.24=.40/.40=1– Jorge’s grade is one standard deviation above the

mean at his school• Susan’s absolute grade is lower but her position

relative to other students at her school is much higher than Jorge’s position at his school

Another Diagram of Normal Curve with Standard Deviation & Z-scores

Discussion of Previous Case

• Relationship of sampling distribution to population (use mean of sample to estimate mean of population)

If Time: Begin Bivariate Statistics (Results with two variables)

• Types of relationships between two variables:– Correlation (or covariation)• when two variables ‘vary together’

– a type of association– Not necessarily causal

• Can be same direction (positive correlation or direct relationship)• Can be in different directions (negative correlation or

indirect relationship)– Independence• No correlation, no relationship• Cases with values in one variable do not have any

particular value on the other variable

Techniques for examining relationships between two variables

• Graphs, scattergrams or plots• Cross-tabulations or percentaged tables• Measures of association (e.g. correlation

coeficient, etc.)

Scattergram (Bivariate)

Tables: Basic Terminology (Tables)

• Parts of a Table– title (conventions)• Order of naming of variables • Dependent, independent, control

– body, cell, column, row– “marginals”

• sources, date

Bivariate Statistics: Parts of the Table

Example of Raw Data Table (computer printout-bivariate)

Regan, T. (1985). In search of sobriety: Identifying factors contributing to the recovery from alcoholism. Kentville, NS.

Another Style of Presentation of Percentaged Tables

Table 1. Percentage in support of strike by type of school

Percent supportingType of School Strike

Secondary 60% (800)

Elementary 30% (1000)

__________________________________________________________N = 1800

Serial NumberDescriptive CaptionDependent Variable

IndependentVariable

Variable

Categories

One category of dichotomousdependent variable

Marginals for independentvariable

Total Sample

Presentation of Percentaged Tables (cont’d)

Table 2. Percentage who support strike by type of school and sex

Sex Female Per cent Male Per cent

Type of School supporting strike supporting strike

Secondary 60% 60% (400) (400)

Elementary 30% 30% (900) (100)

__________________________________________________________Female = .30 : Male = .30 N = 1800

Dependent Variable

IndependentVariable

Controlvariable

Control variable

Categories of control variable

Some Important Factors in Interpretation of Tables

• percentages vs. “raw” frequencies, need to know absolute number of cases (N=)

• grouping categories, missing cases• direction of calculation of percentages (for

bivariate and multivariate statistics)

Collapsing categories (U.N. example)

Babbie, E. (1995). The practice of social researchBelmont, CA: Wadsworth

Collapsing Categories & omitting missing data

Babbie, E. (1995). The practice of social researchBelmont, CA: Wadsworth

Grouping Response Categories

• To make new categories• Facilitate analysis of trends• But decisions have effects on the

interpretation of patterns