1 / 16

Random sampling and probability

Random sampling and probability. Introduction to inferential statistics. Inferential statistics. Review definition: Making a decision about what you do not know -- the population characteristics -- based on what you do know -- the sample data. Two purposes of inferential statistics:

walter
Download Presentation

Random sampling and probability

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Random sampling and probability Introduction to inferential statistics

  2. Inferential statistics • Review definition: Making a decision about what you do not know -- the population characteristics -- based on what you do know -- the sample data. • Two purposes of inferential statistics: • Parameter estimation • Hypothesis testing

  3. The grape Kool-Aid example • Parameter estimation: What is the mean IQ of the population of Grape Kool-Aid drinkers? • Hypothesis testing: Is the mean IQ of the Grape Kool-Aid drinkers different from the mean IQ of the water drinkers?

  4. Which is it? • We want to find the mean amount of pizza eaten by Houghton students. • We want to see if there is a difference in pizza consumption between seniors and sophomores. • We want to see if there is a difference in pizza consumption with vs. without having Pepsi freely available.

  5. Making sense of hypothesis testing: finding your marbles. • Two opaque jars contain marbles. • Jar one contains 50 red marbles and 50 blue marbles. • Jar two contains 90 red marbles and 10 blue marbles. • Drawing one marble at a time from a jar, can you tell which jar it is? Blue Blue Blue Blue Blue Red Red Red Red Red

  6. Random sampling and probability • Two applications of randomization: • Random selection, to produce representative samples • Random assignment, to produce equivalent groups • Random assignment of participants to groups • Random assignment of treatments to groups • Random assignment of sequences of treatments, or levels of the independent variable

  7. Techniques for random sampling • Dichotomous techniques: The coin toss • Multi-group techniques: Random numbers • Computer generated random numbers • Table of random digits • As computer generated random numbers are based on a non-random seed, 1997 saw the development of the lava lamp technique.

  8. A random digits table 12345 67890 12345 67890 12345 1|22864 59302 31334 37506 38477 2|29476 49068 67381 11834 05934 3|39678 89970 09674 83495 99377 4|38476 16459 00794 38457 98032 5|48572 49583 50286 66739 39567 6|68395 58296 96708 92663 49210

  9. Two sampling strategies • Sampling with replacement • Purest form of random selection • Most beneficial for small populations • Sampling without replacement • Less pure random selection • No practical disadvantage for large populations

  10. Probability Theory • A priori probability • p(A) = Number of events classified as A Total number of possible events • For example, the a priori probability of a head on one toss of an unbiased coin is 1 (the number of events classified as heads) divided by 2 (the total number of possible events, heads plus tails) = 1 / 2 = .5

  11. Probability theory... • A posteriori probability • p(A) = Number of times A has occurred Total number of occurrences For example, if I toss any coin ten times, and I get 4 heads, the a posteriori probability of heads is 4 / 10 = .4 • Hypothesis testing compares a posteriori probability with a priori probability.

  12. Probability theory... • Mutual exclusivity and the addition rule • p(A or B) = p(A) + p(B) - p(A ‘n’ B) For example, the probability of drawing a heart or a 3 from a deck of playing cards = 13/52 + 4/52 - 1/52 = 16/52 = .308 The probability of drawing either a heart or a spade from a deck of playing cards = 13/52 + 13/52 – 0/52 = 26/52 = .500

  13. Probability theory... • Combination and the multiplication rule • p(A and B) = p(A) * p(B|A) For example, the probability of drawing a heart and a spade on two successive draws (with replacement) is (13/52)*(13/52) = .0625 and the probability of getting three heads on three tosses of an unbiased coin, simultaneously or sequentially, is .5*.5*.5 = .125

  14. Independent vs dependent events • p(A and B) = p(A) * p(B|A) For example, the probability of drawing a heart and a spade on two successive draws (without replacement) is (13/52)*(13/51) = .0637

  15. Resampling • Resampling is the basis for determining the variability of sample statistics. • Form an initial sample from the population without replacement. • Resample with replacement, drawing samples of the same size as the initial sample and drawing from the initial population.

  16. Probability problems as Z-scores • For many probability problems, Z-score analysis is just the ticket.

More Related