LEARNING PROGRAMME Types of data and descriptive statistic Intermediate Training in Quantitative...

LEARNING PROGRAMME

Types of data and Types of data and descriptive statisticdescriptive statistic

Intermediate Training in Quantitative Intermediate Training in Quantitative Analysis Analysis

Bangkok 19-23 November 2007Bangkok 19-23 November 2007

LEARNING PROGRAMME - 2

Topics to be covered in this presentation

Data collection and variable types

Basic descriptive analysis Review of mean, median, mode, range,

frequencies, crosstabs Multiple response


Learning objectives

By the end of this session, the participant should be able to:Define variable typesConduct basic descriptive statistics for continuous and categorical variablesConduct multiple response tests


In the social sciences we are usually interested in discovering something about a phenomenon.

Whatever the phenomenon we desire to explain, we seek to explain it by collecting data from the real world and then using these data to draw conclusions about what is being studied.


When collecting data…

We rely on two types of variables

1. Continuous2. Categorical

variables provide us information on individuals, households, administrative areas, or meteorological stations, etc


Continuous variableThey assume numeric values, expressed in a given unit of measurement

Income, mm. of rainfall, amount of agricultural production, percent of food insecure hhs, Weight-for-height z-score for children etc.

Most importantly, each number (within a variable) has a meaning in relation to the other numbers, allowing arithmetic comparisons to be drawn


Type of variables

CATEGORICAL CONTINUOUS

Nominal

Ordinal

Interval

Ratio


Types of variables:different levels of measurement

IntervalAn interval scale differs from an ordinal one in that the differences between adjacent categories are equal. Examples include the Fahrenheit and Celsius temperature scale.

Ratio A ratio scale differs from an interval one in that there is a true zero point (% of HHs food insecure).


Distribution of continuous variables

Continuous variables can either be symmetrically distributed (ie normally distributed) or asymmetrically distributed (otherwise known as skewed)Note: To assess a variables distribution in spss, use the “histogram” option under graphs (spss

help can provide more details)

A normal distribution looks

like this…


Distribution of continuous variables…

A skewed distribution looks like this…as this shows, distributions can be both positively and negatively skewed


Lets take a look at two examples…

Income

Weight for height z-scores


Categorical variables

Values are categories, taking a limited set of values

Ex. Child age groups– 0-11, 12-23, 24-35, 36-47, 48-59 months; Sex of respondent- male/female

Categories can be denoted by numbers/ alphabeticallyCategorical variables take 2 forms-- nominal and ordinal variables.


Type of variables

CATEGORICAL CONTINUOUS

Nominal

Ordinal

Interval

Ratio


Nominal variables

A nominal measurement scale is a set of mutually exclusive categories that varies qualitatively but not quantitatively, for example gender, provinces, income sources, etc.

Codes are labels representing different behaviours/ characteristics and they do not imply any underlying order

Variables with a "yes-no“ answer, “male” or “female”


Ordinal categorical variablesAn ordinal measurement scale differs from a nominal one in that the order among the original categories is preserved in the analysis. However differences between adjacent categories are not equal.

Examples social class and perception (bad – medium – good).


Descriptive statistics

Descriptive statistics are the most basic from of statistics

They include: Summaries of one variable Comparisons of two or more variables

These tests are the foundation for more advanced statistical techniques


Descriptives

Continuous variables Range Mean Median Mode

Categorical variables Frequencies Crosstabs


First lets discuss descriptives for continuous variables…


Range

It is the spread between the smallest and the largest values in a distribution


MeanThe mean is a measure of the variable’s central tendency

The (arithmetic) MEAN is the sum of all the values divided by the numbers of cases

Statistics such as mean assume normal distributions


Median

The MEDIAN is the value above and below which half the cases fall, the 50th percentile, i.e. the middle value of a set of observations ranked in order.

The median is a measure of central tendency not sensitive to outlying values--unlike the mean, which can be affected by a few extremely high or low values.

A median does not necessarily assume an normal distribution


Mode

The MODE of a distribution is the value of the observation occurring most frequently. It can be used with all measurement scales.

If several values share the greatest frequency of occurrence, each of them is a mode.


To illustrate these concepts…

Looking at age data from 10 individuals…

What is the range? 12 to 38 What is the mean? 27.2 What is the median? 28 What is the mode? 28

1 2 3 4 5 6 7 8 9 10

12 19 23 26 28 28 28 34 36 38

Papavero

insert animation


Other basic concepts that must be understood…

Variance

Standard deviation


Standard deviation and variance

The standard deviation is the average error between the mean and the observations made (and so is a measure of how well the mean describes the actual data).

The variance is square of the standard deviation

1


Variance and standard deviation

1 2 3 4 5 6 7 8 9 10

12 19 23 26 28 28 28 34 36 38

What is the standard deviation of age??

What is the variance??


Standard deviation

In a normal distribution, 68.27% of cases fall within ± one standard deviation of the mean, 95.45% of cases fall within ± two standard deviations and 99.73% fall within ± three standard deviations.

For example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25 and 65 in a normal distribution.


Standard deviation


Now lets discuss descriptives for categorical variables…


Analysing categorical data

If you want to look at the relationship between two categorical variables:

Cannot use the mean and median

The mean of a categorical variable is completely meaningless because the numeric values we attach to different categories are arbitrary


Descriptives for categorical data

The most basic descriptive for categorical variables are frequencies

which shows the number (or percent) of cases in each category

WAZPREV

4290 11.2 80.2 80.2

1058 2.8 19.8 100.0

5348 14.0 100.0

32840 86.0

38188 100.0

Not malnourished

Malnourished

Total

Valid

SystemMissing

Total

Frequency Percent Valid PercentCumulative

Percent


Descriptives for categorical data

Second, we can also cross tabulate categories from one variable with categories from a second variable, this is known as a contingency table


Contingency TablesChild Gender * underweight Crosstabulation

underweight Total

no yes

Child Gender Male Count 793 280 1073

% within Child Gender 74% 26% 100%

% within underweight 51% 53% 51%

% of Total 38% 13% 51%

Female Count 772 253 1025



% of Total 37% 12% 49%

Total Count 1565 533 2098



% of Total 75% 25% 100%


Contingency Tables

Orphan

TotalNo Yes

Residence Capital, large city Count 1,071 125 1,196

% within residence 89.5% 10.5% 100.0%

% within orphan 7.4% 6.8% 7.3%

Small city Count 395 37 432



Town Count 824 131 955



Countryside Count 12,252 1,558 13,810


% within orphan 84.3% 84.2% 84.2%

Total Count 14,542 1,851 16,393


% within orphan 100.0% 100.0% 100.0%


Example…

What percentage of orphans are malnourished?

What percentage of non orphans are malnourished?

What percentage of malnourished children are orphans?

WAZPREV * ORPHAN Crosstabulation

3995 207 4202

95.1% 4.9% 100.0%

80.2% 80.9% 80.2%

987 49 1036

95.3% 4.7% 100.0%

19.8% 19.1% 19.8%

4982 256 5238

95.1% 4.9% 100.0%

100.0% 100.0% 100.0%

Count

% within WAZPREV

% within ORPHAN

Count

% within WAZPREV

% within ORPHAN

Count

% within WAZPREV

% within ORPHAN

Not malnourished

Malnourished

WAZPREV

Total

Non orphan Orphan

ORPHAN

Total


Multiple response analysis

Sometimes we have to analyze categorical data, where households are able to give more than one response to a question (ex. livelihoods, coping strategies, etc)

Analyzing such data requires a multiple response analysis


After completing question SCM1, complete one incident at a time (line by line), each time repeating the questions above

SCM 2.By order of importance, what incidents did your household experience in the last 1 YEARIncidents code: 1 = Insecurity, Violence2 = Increased price for food4 = Drop in farm gate price5 = Floods6 = drought/dry spell7 = crop pest and disease8 = Livestock disease9 = Sickness of household Member10 = Death of household member11 = Increased household size (IDPs)12 = Loss / lack of employment

SCM 3. What is the main action your household took to compensate the effect of that incident?Coping code: 0 = Nothing1 = Eat less preferred foods2 = Eat fewer or smaller meals per day3 = Go one entire day without meals4 = collect wild foods, hunt or harvest immature crops5 = Distress sale / slaughter of livestock6 = Distress sale of other assets7 = Purchase food on credit8 = Borrow food from families and friends, kinship support9 = Worked for money10 = Worked for food only11 = Reduced expenditures on health or education12 = spent savings13 = Some household members migrated14 = Other (specify)_____________

SCM 4.How often did you do this in the last 1 YEAR?

SCM 5.Did your Household Recover from that incident?

MAIN : (Code) ___ (Code) ___ ___ times

1. Yes

2. No

SECOND : (Code) ___ (Code) ___ ___ times

1. Yes

2. No

THIRD : (Code) ___ (Code) ___ ___ times

1. Yes

2. No

FOURTH : (Code) ___ (Code) ___ ___ times

1. Yes

2. No

FIFTH : (Code) ___ (Code) ___ ___ times

1. Yes

2. No


Multiple response frequencies$shocks Frequencies

2418 12.5% 36.0%

2115 11.0% 31.5%

881 4.6% 13.1%

1410 7.3% 21.0%

2695 14.0% 40.1%

2031 10.5% 30.3%

1479 7.7% 22.0%

2950 15.3% 43.9%

1229 6.4% 18.3%

689 3.6% 10.3%

1398 7.2% 20.8%

19295 100.0% 287.4%

Insecurity, violence

Higher prices

Drop in farmgate price

Floods

Drought

Crop pest/disease

Livestock disease

Sickness in HH

Death in HH

Increased HH size (IDPs)

Loss/lack of employment

$shocksa

Total

N Percent

Responses Percent ofCases

Groupa.


N is the number of households that reported a shock

The Percent column reports the percentage of total responses represented by each shock. This is not easily available from individual frequency tables.

The Percent of Cases column is the percentage of valid cases represented by each shock.


Multiple response crosstabs$shocks*fcgbivariate Crosstabulation

726 1516 2242

32.4% 67.6%

710 1269 1979

35.9% 64.1%

275 536 811

33.9% 66.1%

494 787 1281

38.6% 61.4%

911 1607 2518

36.2% 63.8%

646 1227 1873

34.5% 65.5%

414 946 1360

30.4% 69.6%

764 2050 2814

27.1% 72.9%

341 822 1163

29.3% 70.7%

187 451 638

29.3% 70.7%

431 869 1300

33.2% 66.8%

1887 4467 6354

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

% within $shocks

Count

Insecurity, violence

Higher prices

Drop in farmgate pri

Floods

Drought

Crop pest/disease

Livestock disease

Sickness in HH

Death in HH

Increased HH size (I

Loss/lack of employm

$shocks

Total

poor/borderline food

acceptablefood cons

fcgbivariate

Total

Percentages and totals are based on respondents.

Groupa.


Multiple response… To set up a multiple response in spss…

Click on “Analyze” Click on “Multiple response” Click on “Define sets…” Move the variables of interest into the box in box on

the right Then define the range of the variable Then name the variable Then click on “Add” Then click on “Close”


Multiple response…To run a multiple response in spss…

Click on “Analyze”Click on “Multiple response”Click on “frequencies…” or “crosstabs…”

(whichever descriptive test you would like to conduct)

Move the variables into the proper boxesThen click “Okay”


now practical exercises…..

LEARNING PROGRAMME Types of data and descriptive statistic Intermediate Training in Quantitative...

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