POLI 205

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POLI 205

2. Examining Data

What is a variable?

Anything that can take on different values.

Not Constant

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Continuous Variables

Infinite Range of Numbers

Measurement is always an approximation.

Discrete Variables

Between any two values is nothing.

Whole only (Children)

Exact Measurement

Nominal, Ordinal, or Dichotomous

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Nominal

Named categories

Catholic

Jewish

Muslim

Buddhist

Shinto

Scientologist

Ordinal

Ranking

Strongly Disagree

Disagree

Neutral

Agree

Strongly Agree

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Dichotomous Variables

The presence of a trait or characteristic

Male

Can be created from any variable type

Cutpoints

Collecting Data: Levels of Measurement

• Nominal – Values differ in category or type

• Ordinal – Values placed in order relative to other

values

• Interval – Values equally spaced on a numeric

continuum

• Ratio – Interval variables with a true zero point

Howard T. Tokunaga, Fundamental Statistics for the Social and Behavioral Sciences © SAGE Publications, 2016

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Examining Data Using Tables Frequency distribution table

– Summarizes frequency (f) and percentage (%) of participants for different values of the variable

Lottery ticket f %

Sequence 1 5%

Pattern 6 27%

Nonequilibrated 3 14%

Random 12 54%

Total 22 100%

Examining Data Using Figures Nominal and ordinal data: Bar charts and pie charts

– Bar chart: Bars represent frequency or percentage of each value of the variable

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Examining Data Using Figures Nominal and ordinal data: Bar charts and pie charts

– Pie chart: Area of circle represents percentage of sample corresponding to each value of the variable

Examining Data Using Figures Interval and ratio data: Histograms and frequency polygons

– Histogram: Bars represent frequency of values

– Bars touch each other, indicating numeric continuum

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Examining Data Using Figures Interval and ratio data: Histograms and frequency polygons

– Frequency polygon: Line graphs with connected data points to represent frequencies

Howard T. Tokunaga, Fundamental Statistics  for the Social and Behavioral Sciences © 

SAGE Publications, 2016

Drawing Inappropriate Conclusions

Poorly designed figures can lead to inappropriate or misleading conclusions

Howard T. Tokunaga, Fundamental Statistics  for the Social and Behavioral Sciences © 

SAGE Publications, 2016

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Describing Distributions Modality

– Value(s) of variable with greatest frequency

Symmetry – Symmetric distribution: Frequencies change in

a similar manner moving away from the mode

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Asymmetric distribution: Frequencies change in a different manner moving away from the mode

Variability – Amount of differences in distribution of a variable

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Normal distribution – Unimodal

– Symmetrical

– Neither peaked nor flat