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Statistics: An Introduction Alan Monroe: Chapter 6

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Why Levels of Measurement are Important Levels of measurement are important because they tell us (and any computer program you might use) the specific values we have assigned for certain data. Most computers will interpret numerical values as interval, but you might be defining or using it as nominal or ordinal data.

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What is a Statistic? (88) Numerical Measurement that Summarizes Data It is a “numerical measurement that summarizes some characteristic of a larger body of data. That is why statistics are useful. They can reduce very large amounts of information…to single numbers that convey information you need.” Examples of Statistics: Totals: total population, total for dinner Proportion: could be a fraction, a percentage Rates: miles per gallon Average (or mean)

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Univariate Statistics (90) Measures of Central Tendency: Averages Mean: The mean is computed by adding up all of the individual values and dividing by the number of cases. Can only be computed for Interval Data. Median: Median is the middle: “half cases have higher values and half have lower values.” Often used to calculate income. Mode: (Applies to Nominal, Ordinal, and Interval) It refers to the “most frequently occurring value or category.

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Univariate Statistics (91) Measures of Dispersion: It is a measure of “how closely or widely cases are separated on a variable.” Examples: Range: the difference between the highest and the lowest. Standard Deviation: is based on the summation of the difference of each case from the mean.

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The Concept of Relationships (92) Contingency Tables: (Cross-Tabulation) This is a table showing the frequencies of each combination of categories on the two variables. Can be used to present nominal (party, gender, age) and ordinal data. Scattergrams: (Scatterplots) Relationships between two interval variables are shown in scatterplots. Enables you to present interval data. …

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Multivariate Statistics (98) Strength of a Relationship: How good of a predictor is the IV of the DV. What is the strength of the association? Is there a correlation between the two variables? Direction of a Relationship: Is it a positive or negative relationship? When the IV increases, does the DV increase (positive) or decrease (negative)? Significance: “probably caused by something other than mere chance.” source: http://www.m-w.com/dictionary/significant

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