MATH 117 ­ Applied StatisticsWednesday, 2­8­12

Note that online assignment 5.2 is due today, Feb. 8; assignments 4.1 and 4.2 are due Monday, Feb. 13; assignment 4.3 is due Tuesday, Feb. 14; and assignments 6.1 and 6.2 are due Wednesday, Feb. 15. The unit 1 exam is Monday, Feb. 13.

There are many examples of inaccurate and therefore worthless studies as a result of various biases.

Title: Aug 28 ­ 6:06 AM (1 of 14)

In designing an experimental study why is the selection of the control and treatment groups so important?

Can the split be done by gender?

Can the split be done by volunteers?

Can the split be done alphabetically?

It is best to "randomize" the groups.

Sometimes there is a conscious attempt to "balance" the groups, eliminating any potential lurking variables. (gender, age, education, geography, politics, religion, etc.)

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We find the mean of a discrete set of numbers by adding and dividing by the number of numbers, but what if the numbers are not equally likely in the distribution?

The mean (i.e. expected value) of a discrete distribution is the sum of the products of each value times its probability.

Consider the number of siblings of each of 10 people.

0 1 1 1 2 3 3 5 6 8

P(1) = 3/10 P(5) = 1/10 P(7) = 0

The mean is (0+1+1+1+2+3+3+5+6+8)/10 = 30/10 = 3

Title: Feb 7 ­ 8:53 PM (6 of 14)

To graph this discrete probability distribution (histogram):

Consider the following discrete random variable.

Title: Feb 7 ­ 9:13 PM (7 of 14)

mean = 0 (.23) + 1 (.38) + 2 (.22) + 3 (.13) + 4 (.03) + 5 (.01) + 6 (0) = 1.38

That is, if the total number of home runs from many games is added and divided by the number of games, you'd expect to get approximately 1.38.

Title: Feb 7 ­ 9:16 PM (8 of 14)

Consider the discrete variable determined by the product of 2 rolls of a die.

The mean is 12.250. This is sometimes referred to as the expected value of the variable.

Title: Feb 7 ­ 9:17 PM (9 of 14)

HH = $10 HT or TH = $2 TT = $1

Consider a wager in which a coin in flipped twice with the following payouts.

What is the expected value (mean) of any given wager? What is the "break­even point" for the cost of playing the game?

Title: Feb 7 ­ 9:18 PM (10 of 14)

The Publishers' Clearing House Sweepstakes has a payout of $10,000,000 but a probability of winning of 1 in 505,000,000.

Therefore the expected value is

$1,000,000 x 1/505,000,000 + ­ $.44 x 504,999,999/505,000,000 = ­$.42

Title: Feb 7 ­ 9:20 PM (11 of 14)

By considering many small intervals, we can convert a distribution of a continuous variable to a discrete distribution, which we in turn approximate as a smooth continuous graph.

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Continuous variable to discrete distribution to continuous bell curve.

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Topics for Unit 1 Review:1. General terminology ­ categorical vs. quantitative, discrete vs. continuous, sample vs. population, statistic vs. parameter, descriptive vs. inferential; explanatory vs. response variables2. Statistical measures ­ mean, mode, median, Q1, Q3, range, interquartile range (IQR), standard deviation, outlier3. Graphing ­ dot plot, pie chart, histogram, stem­and­leaf, box­and­whisker4. Normal distribution (bell curve) ­ skewed left or right, z­score, empirical rule5. Probability ­ sample space, probability of events, expected value (mean), independent vs. dependent trials6. Language of studies ­ observational vs. experimental, control group, placebo, single blind, double blind, sample bias, non­response bias, response bias, random sample, sample size, margin of error7. Contingency tables for two categorical variables

Title: Feb 7 ­ 9:21 PM (14 of 14)