Apr. 9 Statistic for the day: Number of times a Hummer H2 could be driven around the world on the excess calories Americans consume each year: 244 Assignment: Review for Monday’s test using practice problems, exercises from book, and lecture notes These slides were created by Tom Hettmansperger and in some cases modified by David Hunter Source: Harper’s index

You should read and review the difference between Categorical and measurement variables Continuous measurement variables and discrete measurement variables You should be able to distinguish among Validity of a measurement Reliability of a measurement Bias of a measurement See pp40-43 of the text

Categorical, discrete measurement, or continuous measurement? Eye color Eye color Weight Weight Number of siblings Number of siblings Gender Gender Time in 100-meter dash Time in 100-meter dash Number of cigarettes smoked in a day Number of cigarettes smoked in a day Building where your first class occurs Building where your first class occurs (Cat)(CM)(DM)(Cat)(CM)(DM)(Cat)

Consider a clock that’s 5 minutes fast. Valid or invalid? Valid or invalid? Reliable or unreliable? Reliable or unreliable? Biased or unbiased? Biased or unbiased? Answer: valid, reliable and biased.

Consider a scale that is sometimes several pounds too low, sometimes several pounds too high Valid or invalid? Valid or invalid? Reliable or unreliable? Reliable or unreliable? Biased or unbiased? Biased or unbiased? Answer: valid, unreliable and unbiased.

Confidence intervals All confidence intervals look like this: Estimate of population value ± (multiplier)(SD of estimate) 1.Know how to match up estimate with SD (three possibilities) 2.Know how to find the multiplier on p. 137 if I give you a confidence coefficient other than 95% (for 95%, the multiplier is 2). By the way, p. 137 will be provided for you on the test (you don’t need to copy it onto your sheet of notes).

How to create 95% CI’s for: a) A population proportion b) A population mean c) The difference between two population means Sample proportion ± 2(SD of sample proportion) Sample mean ± 2(SD of sample mean) Diff of sample means ± 2(SD of diff of sample means) (SE mean)

SD of sample proportion The standard deviation of the sample proportion is estimated by:

SD of sample mean (SE mean) The standard deviation of the sample mean is estimated by This estimate of the SD is called the STANDARD ERROR OF THE MEAN, or sometimes SE mean or SEM.

SD of difference of sample means The standard deviation of the difference between two sample means is estimated by (To remember this, think of the Pythagorean theorem.)

The logic of confidence intervals What does a 95% confidence interval tell us? (What’s the correct way to interpret it?) IF (hypothetically) we were to repeat the experiment many times, generating many 95% CI’s in the same way, then 95% of these intervals would contain the true population value. Note: The population value does not move; the hypothetical repeated confidence intervals do.