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Statistical Reasoning Chapter 1, Lecture 3 “To be an educated person today is to be able to apply simple statistical principles to everyday reasoning. One needn’t memorize complicated formulas to think more clearly and critically about data.” - David Myers Statistical Reasoning Statistical procedures analyze and interpret data allowing us to see what the unaided eye misses. Composition of ethnicity in urban locales Statistical Reasoning in Everyday Life Doubt big, round, undocumented numbers as they can be misleading and before long, become public misinformation. Apply simple statistical reasoning in everyday life to think smarter! Describing Data A meaningful description of data is important in research. Misrepresentation may lead to incorrect conclusions. Measures of Central Tendency Mode: The most frequently occurring score in a distribution. Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by the number of scores that were added together. Median: The middle score in a rank-ordered distribution. Measures of Central Tendency A Skewed Distribution Measures of Variation Range: The difference between the highest and lowest scores in a distribution. Standard Deviation: A computed measure of how much scores vary around the mean. Standard Deviation Page 36 Normal Curve A symmetrical, bell-shaped curve that describes the distribution of many types of data (normal distribution). Most scores fall near the mean. Remember the 68-95-99.7 rule??? Illusion of Control That chance events are subject to personal control is an illusion of control fed by: 1. Illusory Correlation: the perception of a relationship where no relationship actually exists. 2. Regression Toward the Mean: the tendency for extremes of unusual scores or events to regress toward the average. Making Inferences A statistical statement of how frequently an obtained result occurred by experimental manipulation or by chance. Making Inferences When is an Observed Difference Reliable? 1. Representative samples are better than biased samples. 2. Less-variable observations are more reliable than more variable ones. 3. More cases are better than fewer cases. Making Inferences When is a Difference Significant? When sample averages are reliable and the difference between them is relatively large, we say the difference has statistical significance. It is probably not due to chance variation. For psychologists this difference is measured through alpha level set at 5 percent. Interesting Statistical Facts Given any two people in the United States, how many intermediaries are necessary, on the average, before the two are in communication, assuming that the intermediaries may only contact people they know on a first-name basis? 5 people Imagine a huge piece of paper about the thickness of one textbook page. If it were folded in half 50 times, how thick would it be? About 50,000,000 miles Interesting Statistical Facts Assuming a world population of about 6.5 billion, if we gathered everyone together and allotted each person a generous two-by-two feet of ground, how large an area would we need? About 933 square miles, considerable less than Rhode Island’s 1545. What if we allowed everyone to sit comfortably in 216 cubic feet (6 feet on a side)? Every human being on earth would fit comfortably into the Grand Canyon. Homework Read p.38-43 Now let’s practice calculating some of our own statistics from the data gathered on Handout 1-12…