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Three Types of Statistical Analysis Stickrath Three Types 1. Standard Deviation – Used for: examination of one set of data – Essential question: How much variability is in my data? – Teaching example: For a class of students, how much did their individual scores vary from the class average? 2. T-test – Used for: comparison of two sets of data – Essential question: Which set of data is higher? – Teaching example: One group of students used computers everyday and a second group of students never used computers, which group scored higher on the exam? 3. Chi-squared Analysis – Used for: comparison of observed data to expected data – Essential question: Does my observed data fit with my expectations? – Teaching example: I expected 15% of my students to score an A, 25% of my students to score a B, 40% of my students to score a C, 15% of my students to score a D, and 5% of my student to score an F. Do the actual scores fit with my expectations? Standard Deviation • An examination of the variability of data – a low standard deviation indicates the data is spread closely around the mean value – a high standard deviation indicates a wider spread around the mean • Which curve fits the large schools? Small schools? Standard Deviation • What does standard deviation mean? – Think of your upcoming exam – If I find a high standard deviation among the scores of my students what does that mean? – If I find a low standard deviation among the scores of my students what does that mean? Standard Deviation • For example, if you wished to see if a red blood cell count was normal, you could see whether it was within 2 SD of the mean of the population as a whole. Less than 5% of all red blood cell counts are more than 2 SD from the mean, so if the count in question is more than 2 SD from the mean, you might consider it to be abnormal. T-test • Used to compare the means of two distinct groups T-test • Comparison must take the variability of the data into account • Otherwise you end up with the Gates mistake Chi-Squared Analysis • Suppose I bet you $1,000 that I can predict whether heads or tails will turn up each time you flip a coin. • The first time I say, “heads” you flip the coin and it is heads. • I got lucky • The second time I say, “heads” you flip the coin and it is heads Chi-Squared Analysis • The third time, fourth time, fifth time, sixth time, seven time, eighth time, and so on I predict heads. Each time you flip heads. • At what point do you suspect that I am using a two-headed coin? • When do you stop chalking it up to chance and accuse me of using a two-headed coin? • You can use statistics to back up your accusations and save yourself $1,000 Three Types 1. Standard Deviation – Used for: examination of one set of data – Essential question: How much variability is in my data? – Teaching example: How many students scored an A, B, C, D, or F on this exam 2. T-test – Used for: comparison of two sets of data – Essential question: Which set of data is higher? – Teaching example: One group of students used computers everyday and a second group of students never used computers, which group scored higher on the exam? 3. Chi-squared Analysis – Used for: comparison of observed data to expected data – Essential question: Does my observed data fit with my expectations? – Teaching example: I expected 15% of my students to score an A, 25% of my students to score a B, 40% of my students to score a C, 15% of my students to score a D, and 5% of my student to score an F. Do the actual scores fit with my expectations?