Describing Univariate Distributions. Learning Goals Use “level of measurement” to decide how to...

Describing Univariate Distributions

Learning Goals

Use “level of measurement” to decide how to describe the variable distribution

Understand frequency distributions

Understand measures of central tendency

Understand measures of dispersion, spread, and variability

Three Little Phrases — Stay Alert!

1. Units of measurement: Standardized and uniform quantities for expressing an amount (e.g., feet/inches or metres; miles or kilometres; years, months, and days; dollars or Euros).

2. Units of analysis: The type of things on which a variable is defined (“cases” in the data file).

3. Level of measurement: Precision of measurement — nominal or ordinal categories (qualitative); interval-ratio (quantitative). (Named categories; rank order; precise and meaningful # — either continuous or discrete.)

Exercise: Describing “Our” Variables for a Class Data File [1]

HEIGHT

What is its level of measurement?

Is a frequency distribution a good idea?

What measures of central tendency are best?

What measures of dispersion/variability are best?

Describing “Our” Variables [2]

DISTANCE FROM CAMPUS






TIME OF COMMUTE






MODE OF TRANSPORTATION






GENDER






NUMBER OF SIBLINGS






EYE COLOUR






BEER ATTITUDE





Can we make this a Likert response scale ( i.e., strongly agree, agree, uhhh, disagree, strongly disagree)? Why are Likert scales unlikeable?


HOW OFTEN DO YOU ATTEND MUSICAL EVENTS?






MOVIE FAVES





Frequency Distributions

Used for nominal and ordinal data; interval-ratio data may need to be grouped.

Compute counts (frequencies) and relative frequencies (proportions expressed as %).

Do not do the cumulative percentages for nominal data!

Don’t get whole number variable values (number of pets) confused with frequencies!

Measures of Central Tendency

For interval-ratio data: Mean, median, mode.

For ordinal data: Median and mode.

For nominal data: Mode.

Mean vs. Median

If the variable distribution is skewed (long tail of extreme values on ONE side), median may be preferable.

Mean and median are obtained in VERY DIFFERENT WAYS.

Mean: See formula provided by Garner (2010, p. 59).

Median: See algorithm and formula provided by Garner (2010, p. 61–62).

Measures of Dispersion/Variability

Range

Standard deviation

Percentile distributions — e.g., interquartile range

For categoric data: Index of diversity and index of qualitative variation (optional). See Garner (2010, pp. 67–69).

How to Compute the Standard Deviation

Very important!

The algorithm (summarized by the formula) needs to be memorized.

See Garner (2010, p. 65).

Work through a few simple examples.

Don’t confuse the SD with the mean deviation or the mean absolute deviation.

Mean and SD of a Proportion

Proportion for a variable with two categories (binary or dichotomous).

Coded as 0/1 for the two categories.

The mean = number of cases coded 1 divided by the total number of cases.

The SD is the square root of [p x (1–p)] where p is the proportion of cases coded 1.

Describing Univariate Distributions. Learning Goals Use “level of measurement” to decide how to...

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