# SOAN 2120 Chapter Notes - Chapter 8: Standard Deviation, Descriptive Statistics, Statistical Inference

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9 Aug 2016

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Department

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Professor

Chapter 8: Analysis of Quantitative Data – page #192-219:

Results With One Variable:

Measures of Central Tendency:

• Researchers often want to summarize the information about one variable into a single

number – they use three measures of central tendency, or measures of the center of the

frequency distribution: mean, median, and mode, which are often called averages (a less

precise and less clear way of saying the same thing)

• The mode is the easiest to use and can be used with nominal, ordinal, interval, or ratio data –

it is simply the most common or frequently occurring number

• The median is the middle point – it is also the 50th percentile, or the point at which half the

cases are above it and half below it; it can be used with ordinal-, interval-, or ratio-level data

(but not nominal level)

o The easiest way is first to organize the scores from highest to lowest, then count to

the middle – if there is an odd number of scores, its simple; if there is an even

number of scores the median is somewhere between the two middle numbers

• The mean, also called the arithmetic average, is the most widely used measure of central

tendency; it can be used only with interval- or ratio-level data

o Compute the mean by adding up all scores, then divide by the number of scores

• If the frequency distributions form a “normal” or bell-shaped curve, the three measures of

central tendency equal each other – if the distribution is a skewed distribution, then the three

will not be equal

• If most cases have lower scores with a few extreme high scores, the mean will be the

highest, the median in the middle, and the mod the lowest – if most cases have higher scores

with a few extreme low scores, the mean will be the lowest, the median in the middle, and the

mode the highest

Level of

Measurement

Measure Of Central

Tendency

Mode

Median

Mean

Nominal

Yes

Ordinal

Yes

Yes

Interval

Yes

Yes

Yes

Ratio

Yes

Yes

Yes

Results with Two Variables:

Bivariate Tables:

What is a Bivariate Table?

• The bivariate continency table is widely used – it presents the same information as a

scattergram in a more condensed form

• The data can be measured at any level of measurement, although interval and ratio data

must be grouped if there are many different values

• The table is based on cross-tabulation; that is, the cases are organized in the table on the

basis of two variables at the same time

• A contingency table is formed by cross-tabulating two or more variables – it is contingent

because the cases in each category of variable get distributed into each category of a second

(or additional) variable

• The table distributes cases into the categories of multiple variables at the same time and

shows how the cases, by category of one variable are, “contingent upon” the categories of

other variables

• Researchers convert raw count tables into percentaged tables to see bivariate relationships –

there are three ways to percentage table: by row, by column, and for the total

1. By row – compute the percentage of each cell as a percentage of the row total

2. By column – when calculating column percentages, compute the percentage each cell is

the column total