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Reasoning in Psychology Using Statistics

Explore the role of sampling and basic probability in psychology statistics. Learn about population versus sample, sampling error, and methods to minimize bias. Discover how to generalize back from data using inferential statistics.

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Reasoning in Psychology Using Statistics

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  1. Reasoning in PsychologyUsing Statistics Psychology 138 2017

  2. Quiz 2 • Quiz 2 due Fri. Feb. 3 (11:59 pm) • Don’t forget Exam 1 is coming up (Feb 8) • In class part – multiple choice, closed book • In labs part – open book/notes • Today • Sampling and basic probability Announcements

  3. Nearly 10,000 responses Do you believe results? Does it reflect population of parents? Is the samplerepresentative of all parents? Ann Landers to readers, “If you had to do it again, would you have children?” (1975-76) 70% said kids not worth it! Sampling Discussion of the 1976 Landers survey

  4. Population Sample Those research is about Subset that participates in research (giving us our data) Sampling

  5. Sampling to make data collection manageable Inferential statistics to generalize back Population Sample Sampling

  6. Population (N=25) For rate hikes Against rate hikes # “for hikes” Proportion “for hikes” in population = Total # 10 = = 0.4 25 Local politician wants to know opinions on proposed rate hikes Sampling

  7. # “for hikes” = Total # Proportion “for hikes” in sample 2 = = 0.4 5 Population (N=25) Sample (n=5) Expect to get sample that matches population exactly? If not: SAMPLING ERROR Sampling

  8. Goals of sampling: • Reduce:Sampling error • Maximize: Representativeness • Minimize: Bias Sampling

  9. Goals of sampling: • Reduce:Sampling error • difference between population parameter and sample statistic BUT we usually don’t know what the population parameter is! • Maximize: Representativeness • Minimize: Bias Sampling

  10. Population (N=25) # “for hikes” = Total # Proportion “ for hikes” in population # “for hikes” Proportion “for hikes” in sample = Total # 2 10 = = 0.4 = = 0.4 5 25 Sample (n=5) parameter statistic Sampling error = 0.4 - 0.4 = 0 Sampling Error

  11. # “for hikes” = Total # Proportion “ for hikes” in population # “for hikes” Proportion “for hikes” in sample = Total # 3 10 = = 0.6 = = 0.4 5 25 Population (N=25) Sample (n=5) parameter statistic Sampling error = 0.6 - 0.4 = 0.2 Sampling Error

  12. Population (N=52) Lots of Samples (hands n=5) Sampling Error: Games of chance http://www.intmath.com/counting-probability/poker.php Lucky numbers: Marcus du Sautoy (~14 mins)

  13. Population (N=52) Sample (n=5) 13 Proportion of spades = 52 in deck = 0.25 1 Proportion of spades = 5 in a draw = 0.20 parameter statistic Sampling error = 0.25 – 0.20 = 0.05 Sampling Error: Games of chance

  14. Population (N=52) Sample (n=5) 13 Proportion of any suit = 52 in deck = 0.25 5 Proportion of suit = 5 in a draw = 1.0 parameter statistic Sampling error = 0.25 – 1.0 = 0.75 Sampling Error: Games of chance

  15. Use sample (statistic) to estimate population (parameter) • Problem: Samples vary • different estimates depending on sample • But we know what affects size of sampling error (can prove mathematically) • Variability in population (+ relationship) • As variability increases, sampling error increases • Size of sample (- or inverse relationship) • As sample size increases, sampling error decreases Formula we will learn later: SE = SD/√n Sampling Error

  16. Goals of sampling • Reduce:Sampling error • difference between population parameter and sample statistic • Maximize: Representativeness • Minimize: Bias • to what extent do characteristics of sample reflect those in population • systematic difference between sample and population Sampling

  17. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling Sampling Methods

  18. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling • Every individual has equal & independent chance of being selected from population 3 2 2 Sampling Methods

  19. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling • Step 1: compute K = population size/sample size • Step 2: randomly select Kth person 22/6 K = 4 4 1 1 Sampling Methods

  20. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling • Step 2: randomly select from each group (proportional to size of group: 8/23=.35 11/23=.484/23=.17) • Step 1: Identify groups (strata) blue green red If n =5, 2 2 1 Sampling Methods

  21. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling • Step 1: Identify groups blue green red • Step 2: pick first # from each group (not proportional) If n =6, 2 2 2 Sampling Methods

  22. 70% of parents say kids not worth it! Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling • Convenience sampling: voluntary response method of sampling • Using easily available participants • Results typically biased • Typical respondents with very strong opinions (NOT representative of population) • Newsday random sample (n = 1373) found 91% said “yes” • For more discussion: David Bellhouse Sampling Methods

  23. Probability sampling Non-probability sampling • Simple random sampling • Systematic random sampling • Stratified sampling • Convenience sampling • Quota sampling Representativeness Good Poor Bias Stacked Deck Sampling Methods

  24. Population Where does “probability” fit in? • Randomness in sampling leads to variability in sampling error • “Randomness” in short run is unpredictable but in long run is predictable! • Odds in games of chance • Allows predictions about likelihood of getting particular samples Possible Samples Inferential statistics

  25. Probability of a sample with particular characteristics Where does “probability” fit in? If we know the proportions in the population And we know how we sampled: Deal 5 cards Probability of 4 of a kind = 0.00024 • Allows predictions about likelihood of getting particular samples Inferential statistics Tools that use our estimates of sampling error to generalize from observations from samples to statements about the populations

  26. b c a C A B • Draw lettered tiles from bag • Bag contains: • A’s B’s and C’s. • Both upper and lower case letters • What is the probability of getting an A (upper or lower case)? Total number of outcomes classified as A Prob. of A = p(A) = Total number of possible outcomes Sample space Basics of probability: Derived from games with all outcomes known

  27. One outcome classified as heads 1 = = 0.5 2 Total of two outcomes What are odds of getting heads? This simplest case is known as the binomial = 21 = 2total outcomes pn=(0.5)1= the prob of a single outcome 2n Flipping a coin example: 1 flip

  28. What are the odds of getting all heads? One 2 heads outcome = 22 = 4total outcomes pn = (0.5)2 = 0.25 for 1 outcome twice in a row 2n = 0.25 Four total outcomes Number of heads 2 1 1 0 Flipping a coin example: 2 flips All heads on 3 flips? 23 = 8 outcomes p3 = (0.5)3 = 0.125 or ⅛

  29. What are the odds of getting only one heads? = 0.50 Four total outcomes Number of heads 2 1 Two 1 heads outcome 1 0 Flipping a coin example: 2 flips

  30. What are the odds of getting at least one heads? Three at least one heads outcome = 0.75 Four total outcomes Number of heads 2 1 1 0 Flipping a coin example: 2 flips

  31. What are the odds of getting no heads? = 0.25 Four total outcomes Number of heads 2 1 One no heads outcome 1 0 Flipping a coin example: 2 flips

  32. What are the odds of being dealt a “Royal Flush”? Total number of outcomes classified as A Prob. of A = p(A) = Total number of possible outcomes 4 = 0.000001539 p(Royal Flush) = 2,598,960 ~1.5 hands out of every million hands Odds in Poker

  33. What are the odds of being dealt a “Straight Flush”? Total number of outcomes classified as A Prob. of A = p(A) = Total number of possible outcomes 40 = 0.00001539 p(straightflush) = 2,598,960 ~15 hands out of every million hands Odds in Poker

  34. What are the odds of being dealt a …? Total number of outcomes classified as A Prob. of A = p(A) = Total number of possible outcomes Odds in Poker

  35. Where does “probability” fit into statistics? • Most research uses samples rather than populations. • The predictability in the long run, allows us to know quantify the probable size of the sampling error. • Inferential statistics use our estimates of sampling error to generalize from observations from samples to statements about the populations. Inferential statistics

  36. Today’s lab: Try out sampling and probability • Questions? Breaking down probability sampling(~4 mins) Sampling: Simple Random, Convenience, systematic, cluster, stratified (~4 mins) Non-Probability Sampling (~4 mins) Basics Probability and Statistics | Khan Academy (~8 mins) Example 2 | Probability and Statistics | Khan Academy (~10 mins) Probability with playing cards | Khan Academy (~10 mins) Wrap up

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