European Social Survey



EUROPEAN SOCIAL SURVEY

I: Levels of Measurement, Measures of Central Tendency and Dispersion

The level of measurement of a variable in mathematics and statistics, also called measurement scale ratings is to describe the nature of the information contained within numbers assigned to objects and, therefore, within a variable. According to the theory of scales of measurement, several different mathematical operations are possible depending on the level at which the variable being measured.

Nominal Level

vote - (Voted last national election)

Vote variable that has been used in the ESS data is an example of Nominal level measurement; it is a categorical variable in nature that differs in quality rather than quantity. Given the observations that are made from reality, you can assign each to a single category or group. Each group or category is labeled with a name or number of arbitrary shape, i.e. it is labeled according to the wishes or convenience of the investigator. This level of measurement is only qualitative and variables are therefore qualitative.

1

Yes

2

No

3

Not eligible to vote

7

Refusal

8

Don't know

9

No Answer

Ordinal Level

trstlgl- (Trust in Legal System)

The variable above mentioned is an example of Ordinal Variable, the ordinal variable can take different values ??on a scale established order, while not necessary that the interval between measurements is uniform, i.e. mild, moderate, severe.

0

No Trust at all

1

“1”

2

“2”

3

“3”

4

“4”

5

“5”

6

“6”

7

“7”

8

“8”

9

“9”

10

Complete Trust

77

Refusal

88

Don't Know

99

No Answer

2 A

Choose one variable measured at the nominal, ordinal, and ratio level from the ESS: calculate appropriate measures of central tendency for all three.

Statistics for Ordinal

trstlgl - (Trust in the legal system)

N

Valid

41531

Missing

1469

Mean

5.04

Median

5.00

Mode

5

Statistics for Nominal

vote - Voted last national election

N

Valid

42497

Missing

503

Mean

1.34

Median

1.00

Mode

1

2 B

Choosing an appropriate variable in the ESS, calculate its inter-quartile range and explain the result.

The inter-quartile range is an adequate measure of variability when the central position measurement employed has been the medium. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1), i.e. IQR = Q3 - Q1.

IQR = 40 - 35

IQR = 5

Statistics

wkhct - Total contracted hours per week in main job overtime excluded

N

Valid

35290

Missing

7710

Mean

37.09

Median

40.00

Mode

40

Percentiles

25

35.00

50

40.00

75

40.00

In ESS (wkhct) is carried out to determine total contracted hours per week in main job excluding the overtime, the inter-quartile range was 5 hours. This meant that the middle 50% of the pupils varied by 5 hours in the amount of contracted hours they spent on overtime. Half of the inter-quartile range is called quartile deviation (DQ): DQ = RQ/2 = (Q3 - Q1)/2. It is used to construct box and whisker plots (box plots) that serve to display the variability of a variable and compare distributions of the same variable, in addition to locating outliers.

2 C

Choosing an appropriate variable from the ESS, calculate its mean and standard deviation and explain the result.

Measures of central tendency (mean, median and mode) serve as points of reference for interpreting Measures of Central Tendency and Dispersion provides a basis for conducting further tests on the data. In order to analyze the measure of central tendency and dispersion for this research paper, data has been taken from the European Social Survey (ESS) Data Disk file ...