Chapter 12
Descriptive Statistics
Outline 
Concepts 
I. Statistics in Communication Research 
descriptive
statistics:
numbers that characterize some information 
A.
Measures of Central Tendency 
measures of
central tendency:
measures that describe what is going on within sample groups or
populations on the average 
B. Measures of Variability or Dispersion 

1. Range 
range: the difference between the highest and lowest scores (range is greatly affected by extreme scores) 
2. Variance 
variance: though computed differently, a measure that attempts to summarize the average of squared differences of scores from the mean, symbolized for the sample variance as s^{2 }and for the population variance s^{2 }. 
3. Standard Deviation 
standard deviation: though computed differently, a measure that attempts to summarize the average deviation of scores from the mean, by estimating such a value from the square root of the variance s^{2}; symbolized for the sample standard deviation as s and for the population standard deviation as s 
II.
Distributions 

1. Types of Skew if the skewness coefficient is positive, then the long tail is “above” or to the right of the “ground zero” mean of the distribution if the skewness coefficient is negative, then the long tail is “below” or to the left of the “ground zero” mean of the distribution 
skew: a measure of centeredness (skewness reveals the side of the distribution in which the longest "tail" lies) 
2. Peakedness of Distributions 
kurtosis:
a measure of peakedness of a distribution (in a perfect normal
distribution, the distribution is as high as three standard deviations
is wide) 
B. Standard Normal Distribution 
the standard normal curve: a probability distribution that tells the expected value that would be obtained by sampling at random 
1.
The Gaussian Curve the standard normal curve can help identify long run expectations we might have for samples we take. 
probability distributions: the theoretical pattern of expected “values of a random variable and of the probabilities of occurrences of these values” (Upton & Cook, 2002, p. 294) data distributions: data collected from actual samples of events 
3. Using
z Scores 
z scores: scores that transform values from other distributions into equivalent units under the standard normal curve with means of 0 and standard deviations and variances of 1.

III. Measures of Association 
correlation:
a measure of the coincidence of variables 
A.
Interpreting Correlations 
in a
scatterplot, researchers often add a line of "best fit" 
calculating proportions of variance explained 
coefficient of determination: the percentage of variation in one variable that can be explained by a knowledge of the other variable alone (computed by squaring a correlation coefficient or computing eta if nonlinear patterns are to be examined) 
B.
Major Forms of Correlations 

1. Pearson Product Moment Correlation 
Pearson product moment correlation: a correlation method is suitable for situations in which both the independent and dependent variables (identified as X and Y respectively in most notation) are interval or ratio level measures 
2. Spearman Rank Order Correlation 
Spearman rank order correlation: a correlation method suitable for situations in which both the independent and dependent variables are ordinal measures 