Statistical Reasoning in Everyday Life

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Presentation transcript:

Statistical Reasoning in Everyday Life There are three kinds of lies. Lies, damn lies, and statistics. - Mark Twain

Module 7 7-1 Describe the three measures of central tendency, and discuss the relative usefulness of the two measures of variation. 7-2 Explain how we know whether an observed difference can be generalized to other populations.

Why do we need statistics? Researchers asked 5522 Americans to estimate the percentage of wealth owned by the richest 20%.... The average guess was 58%. The actual number is 84%... Stats are tools that help us see & interpret what the unaided eye or unscientific guess might miss or mislead Something to remember: Doubt big, round, undocumented numbers. (10% homosexuality)

Descriptive Statistics Numerical data used to measure & describe characteristics of groups. Includes measures of central tendency & measures of variation. Histogram: bar graph depicting a frequency distribution

Percentage Still on Road 100 90 80 70 60 50 Our Brand Brand Brand Brand X Y Z

Measures of Central Tendency Mode: the most frequently occurring score(s) in a distribution Median: the middle score in a distribution, half the scores are above & half below Mean: the arithmetic average of a distribution, obtained by adding the scores & then dividing by the number of scores

Skewed Distributions

Measures of Variation Range: the difference between the highest & lowest scores in a distribution Standard Deviation: a computed measure of how much scores vary around the mean score Wechsler Intelligence Mean=100 SD = 15 Z Score = Number of SD variation (e.g. 145 IQ would be +3

Inferential Statistics Numerical data that allow one to generalize – to infer from sample data the probability of something being true of a population Reliability Representative beats biased Less variable beats more variable (basketball scorer example) More cases beats less (college visit example) Significance Indicates the likelihood that a result will happen by chance, but does NOT say anything about importance of the result (Normally considered to be less than .05)

Find a graph in the popular media or advertisements Find a graph in the popular media or advertisements. How does the source (mis)use statistics to make a point? At the beginning of college, around 100 students will have 100% yet only 10-15 will graduate with perfect grades…. Why??