Chapter 12
Descriptive Statistics
Outline

Concepts

I. Statistics in Communication Research 
descriptive statistics: numbers that characterize some
information inferential statistics: tools that help researchers draw conclusions about the probable populations from which samples did or did not belong 
A. Measures of Central Tendency (Arithmetic Mean, Median, and Mode) 
measures of central tendency: measures that describe
what is going on within sample groups or populations on the average arithmetic mean: (the number most people call "the average") the sum of a set of scores divided by the number of scores unbiased estimator: a sample statistic that is likely to approximate the population parameter median: a score that appears in the middle of an ordered list of scores mode: the most commonly occurring score (bimodal: the condition that occurs when data have two modes) 
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: the average of squared differences of scores from the mean (abbreviated for sample variance s^{2 }and for the population variance s^{2 }[sigma squared]) 
3. Standard Deviation  standard deviation: a measure of the average of how far the scores deviate from the mean (abbreviated s for the sample standard deviation and s for the population standard deviation) 
II. Distributions A. Nonnormal and Skewed Distributions 

1.
Types of Skew (negative or leftward skew; positive or rightward skew) 
skew: a measure of centeredness (skewness reveals the side of the distribution in which the longer "tail" lies) 
2. Peakedness of Distributions 
kurtosis: a measure of peakedness (in a perfect normal
distribution, the distribution is as high as three standard deviations is wide) platykurtic: a very flat distribution mesokurtic: a peaked distribution that is neither very high nor very low leptokurtic: an extremely peaked distribution 
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 characteristics of the curve: median, mean, and mode are all at the same place on the distribution, marked as 0 and symbolized as mu (m). Skewness is 0 and kurtosis is 3 since the distribution is perfectly centered and peaked. Tails never touch bottom. A standard deviation equals 1. 2. Interpreting Areas Under the Normal Curve approximately 2/3rds (68.2%) of the distribution exists from 1s below the mean to 1s above the mean. The standard normal curve can help identify long run expectations we might have for samples we take. 3. Using z Scores researchers can use the standard normal curve to make decisions by changing their sample data into "z scores" (also called standard scores). Z scores permit us to represent data scores as units under the standard normal curve. 
probability distributions: a distribution of the
expected value that would be obtained by sampling an random data distributions: data collected from actual samples of events 
III. Measures of Association  correlation: a measure of the coincidence of variables correlation coefficients can range from 1.00 to 1.00 
A. Interpreting Correlations direct and inverse relationships

direct relationship: a correlation indicating that
as one variable increases, the other variable also 
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 though causal relationships should produce high correlations, a correlation cannot show causation by itself (researchers must use the experimental method or wait for the method of history to resolve matters). 

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 is suitable for situations in which both the independent and dependent variables are ordinal measures 