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Slide 1

LIS 570

Summarising and presenting data - Univariate analysis

Slide 2

Summary

• Basic definitions

• Descriptive statistics

• Describing frequency distributions

• shape

• central tendency

• dispersion

Slide 3

Selecting analysis and statistical techniques

Slide 4

Basic Definitions

• Values : the categories developed for a variable

• Nominal

• Ordinal

• Interval

• Data : Observations (Measurements) taken on the units of analysis

Slide 5

Basic definitions

• Statistics - Methods for dealing with data

• Descriptive statistics

• summarise sample or census data

• Inferential statistics

• Draw conclusions about the population from the results of a random sample drawn from that population

Slide 6

Methods of analysis (De Vaus, 134)

Slide 7

Frequency Distributions

• Ungrouped frequency distribution

• A list of each of the values of the variable

• The number of times and/or the percent of times each value occurs

• Grouped frequency distribution

• A table or graph which shows the frequencies or percent for ranges of values

Slide 8

Frequency distributions

Slide 9

Frequency distributions

• Required information for frequency tables

• table number and title

• labels for the categories of the variables

• column headings

• the number of missing cases

Slide 10

Histograms

Slide 11

Describing Frequency Distributions

• Shape

• Symmetrical (Mirror image)

• Skewed

• Negative skew

• tail toward lower scores

• Positive skew

• tail toward higher scores

• Dispersion

• Central tendency

Slide 12

Shape - for ordinal or interval variables

Slide 13

Shape - for ordinal or interval variables

Slide 14

Shape – Symmetry

Slide 15

Central Tendency

• Typical or representative value or score

• Mean  (arithmetic mean)( x )

• Sum all the observations / n

• Use for interval variables when appropriate

• Median

• Value that divides the distribution so that an equal number of values are above the median and an equal number below           

• Mode

• Value with the greatest frequency Uni-modal, bi-modal etc.

Slide 16

Mode

• Best for nominal variables

• Problems

• most common may not measure typicality

• may be more than one mode

• unstable - can be manipulated

• Dispersion

• variation ratio (v)

• % of people not in the modal category

Slide 17

Median

• Preferred for ordinal variables

• people are ranked from low to high

• median is the middle case

• the median category is the one that the middle person belongs to

Slide 18

Dispersion

• The cth percentile of a set of numbers is a value such that c percent of the numbers fall below it and the rest fall above.

• The median is the 50th percentile

• The lower quartile is the 25th percentile

• The upper quartile is the 75th percentile

• five number summary

• Median, quartiles and extremes

Slide 19

Dispersion

Slide 20

Boxplot

Slide 21

Mean

• uses the actual numerical values of the observations

• most common measure of centre

• makes sense only of interval or ratio data,

• frequently computed for ordinal variables as well.

Slide 22

Dispersion

• The standard deviation and variance measure spread about the mean as centre.

• Variance

• mean of the squares of the deviations of the observations from the mean.

• Standard deviation

• the positive square root of the variance

Slide 23

Example Data (6,7,5,3,4)