Social Statistics and Data Analysis-Lecture 19-Sociology-Dr David Hall, Lecture notes of Social Statistics and Data Analysis

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Measures of Central Tendency

We summarize a variable by finding a

“typical” score.

Measures of Central Tendency are

“typical” scores & represent values

around which others concentrate.

The Mode

The mode is the value with the highest

frequency count or tally.

While the mode can be useful, it only

tells us which value occurred the

most frequently…so it ignores

information on how values are

distributed.

The Mean

 The mean incorporates all of the values for a variable! It is obtained by adding up all the values & dividing that sum by the total number of cases.

 Since it contains the maximum information, the mean is usually the most accurate, stable & useful measure of central tendency….however, it can be distorted by a few extremely high or low values.

Measures of Variability

 A quick measure is the range. To calculate ( R ), subtract the lowest value ( L ) from the highest value ( H ). It is based on the 2 extreme scores, and ignores all other information about the dispersion.

 The variance reflects the sum of deviations of each value from the mean and provide us with an “average” amount of dispersion or variability.

 The standard deviation is the square root of the variance.

From Descriptive to Inferential

Statistics

 The “normal distribution” & z -scores

connect descriptive and inferential

statistics…by adding to the

interpretation of the mean & standard

deviation, and forming the basis for

statistical estimation, hypothesis

testing, measures of association.

Key aspects of the normal curve:

 The normal curve is symmetrical or bell- shaped.

 The average (mean) is also the most frequently occurring value (the mode), and the value that splits the distribution in half (the median).

 Assuming a variable is normally distributed we can say more about the standard deviation.

Hypothesis Testing: t-tests

If we are interested in testing if the

means or proportions of a variable

differ between two groups , the t-ratio

or t-test is our statistic of choice.

 If testing for differences in the means of 3+ groups, your choice is analysis of variance (ANOVA).

 SSt = Total Sum of Squares (total Variation in data). SSb = Between Group Sum of Squares (between group variation in data). SSw = Within Group Sum of Squares (within group variation in the data).

 The F-ratio is the difference between the groups relative to the difference within the groups we are comparing.

Analysis of Variance (ANOVA)