Semester 2: Lecture 3

Quantitative Data Analysis: Univariate Analysis II

Prepared by: Dr. Lloyd Waller ©

Quantitative Data Analysis

• There are several reasons researchers use statistics in their research.– To describe– To identify relationships– To determine if there are differences– To identify other variables that may be

impacting on the research

To Describe

• Descriptive statistics are used to provide an overview of the data

• Typically, the population being studied is described statistically. This helps the reader of the research to see if the research can be generalized to other groups.

Characteristics of the distribution

• Measures of central tendency– Mean– Median– Mode

• Measures of dispersion– Range– Standard Deviation

Choosing a Descriptive Statistics

• Show table taken from Research Methods in Politics (p. 127).

Measures of Central Tendency

• used to indicate the value that is reprehensive

• the one value or score that best represents the entire set of cases on a variable.

Measures of Dispersions.

• tells us whether the variation around the average value we have identified is limited

• whether the variation is so great that the most typical case is not really very representative of the population at all

The use of each level of measurement is governed by certain rules associated with levels of measurements.

Measures for Nominal Variables

•A Measure of Central Tendency•Value that Occurs Most Often•Not Affected by Extreme Values•There May Not be a Mode•There May be Several Modes•Used for Either Numerical or Categorical Data

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Mode = 9

0 1 2 3 4 5 6

No Mode

THE MODE

An Example: The Mode

Table 1: Gender of respondents

Frequency Percent Valid PercentCumulative

Percent

Valid 1=male 150 69.4 69.4 69.4

2=female66 30.6 30.6 100.0

Total 216 100.0 100.0

Of the sampled population (n=216), 69.4% were males compared to 30.6% females.

Measures for Ordinary Variables

The Median

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Median = 5 Median = 5

•Important Measure of Central Tendency

•In an ordered array, the median is the “middle” number.

•If n is odd, the median is the middle number.•If n is even, the median is the average of the 2

middle numbers.•Not Affected by Extreme Values

Measures for Interval Variables

The Mean (Arithmetic Average)

•It is the Arithmetic Average of data values:

•The Most Common Measure of Central Tendency

•Affected by Extreme Values (Outliers)

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 12 14

Mean = 5 Mean = 6

N Valid 216

Missing 0

Mean 20.33

Median 20.00

Mode 20

Std. Deviation 1.692

Skewness 2.868

Std. Error of Skewness .166

An Example: The Median Mean

Conclusion• Descriptive Statistics are a resourceful tool in the

political scientist’s toolkit, either as a preliminary part of subsequent, more sophisticated analysis of as stand alone research

• The particular criticism that is often made of statistics is that, as a form of information, it fails to capture the richness an complexity of the political world. Skeptics argue, with some justification, that the validity of quantitative measurements (that is, the extent to which such measurements manage to capture whatever it is that they are intended to measure) is questionable.

Shape

• Describes How Data Are Distributed

• Measures of Shape: • Symmetric or skewed

Right-SkewedLeft-Skewed SymmetricMean = Median = ModeMean Median Mode Median MeanMode

• Skewness refers to the degree and direction of asymmetry in a distribution.

No Skew

Positively (skewed to the right) Skewed

Negatively (left) Skewed