1. Reasoning in Psychology Using Statistics Psychology 138 2015

2. Reasoning in Psychology Using Statistics Announcements Don’t forget Quiz 5 is due Fri. Mar. 20 at midnight

3. Reasoning in Psychology Using Statistics Testing Hypotheses –Step 1: State your hypotheses –Step 2: Set your decision criteria –Step 3: Collect your data from your sample –Step 4: Compute your test statistics –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program Note: In the labs I combine steps 1 & 2, so it is described as a 4 step program

4. Reasoning in Psychology Using Statistics Testing Hypotheses –Step 1: State your hypotheses –Step 2: Set your decision criteria –Step 3: Collect your data from your sample –Step 4: Compute your test statistics –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program

5. Reasoning in Psychology Using Statistics Distribution of sample means A simpler case –Population: –All possible samples of size n = 2 2468 2 4 62 2 82 2 44 4 6 8 28 8 8 8 8464 6 6 6 6 4 6 8 242 mean 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 There are 16 of them

6. Reasoning in Psychology Using Statistics Distribution of sample means 2 4 6 8 2 4 6 8 2 46 2 6 2 6 46 4 6 8 28 8 8 8 4 4 4 6 8 2 2 mean 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 means 2345678 5 2 3 4 1 In long run, the random selection of tiles leads to a predictable pattern The distribution of sample means

7. Reasoning in Psychology Using Statistics Distribution of sample means means 2345678 5 2 3 4 1 Xfp 810.0625 720.1250 630.1875 540.2500 430.1875 320.1250 210.0625 Sample problem: –What is the probability of getting a sample (n = 2) with a mean of 6 or more? P(X > 6) =.1875 +.1250 +.0625 = 0.375 Same as before, except now we are asking about sample means rather than single scores Using the distribution of sample means Finding out how likely is a particular sample

8. Reasoning in Psychology Using Statistics Distribution of sample means Distribution of sample means is a “ virtual ” distribution between the sample and population –Note: There is a different one for each sample size PopulationDistribution of sample meansSample Shape Center Spread

9. Reasoning in Psychology Using Statistics Properties of the distribution of sample means Shape –If population is Normal, then the dist of sample means will be Normal –If the sample size is large (n > 30), the DSM will be approximately Normal ( regardless of shape of the population) Population Distribution of sample means n > 30

10. Reasoning in Psychology Using Statistics –The mean of the dist of sample means is equal to the mean of the population PopulationDistribution of sample means same numeric value different conceptual values Center Properties of the distribution of sample means

11. Reasoning in Psychology Using Statistics Center –The mean of the dist of sample means is equal to the mean of the population –Consider our earlier example 2468 Population μ = 2 + 4 + 6 + 8 4 = 5 Distribution of sample means means 2345678 5 2 3 4 1 2+3+4+5+3+4+5+6+4+5+6+7+5+6+7+8 16 = = 5 Properties of the distribution of sample means

12. Reasoning in Psychology Using Statistics Spread Standard deviation of the population Sample size Properties of the distribution of sample means –The Stand. Dev. of the Distrib. of Sample Mean depends on 2 things

13. Reasoning in Psychology Using Statistics Spread Standard deviation of the population μ X 1 X 2 X 3 μ X 1 X 2 X 3 –The smaller the population variability, the closer the sample means are to the population mean, so the smaller the spread of sample means Properties of the distribution of sample means

14. Reasoning in Psychology Using Statistics Sample size μ n = 1 X Properties of the distribution of sample means Spread Standard deviation of the population

15. Reasoning in Psychology Using Statistics μ n = 10 X Properties of the distribution of sample means Sample size Spread Standard deviation of the population

16. Reasoning in Psychology Using Statistics μ n = 100 X - The larger the sample size the smaller the spread of sample means Properties of the distribution of sample means Sample size Spread Standard deviation of the population

17. Reasoning in Psychology Using Statistics Spread Standard deviation of the population Sample size –Putting them together we get the standard deviation of the distribution of sample means –Commonly called the standard error Properties of the distribution of sample means - The smaller the population variability, … the smaller the spread - The larger the sample size the smaller the spread

18. Reasoning in Psychology Using Statistics Properties of the distribution of sample means All three of these properties are combined to form the Central Limit Theorem –For any population with mean μ and standard deviation , the distribution of sample means for sample size n will approach a normal distribution with a mean of μ and a standard deviation of as n approaches infinity (good approximation if n > 30). MEMORIZE THIS

19. Reasoning in Psychology Using Statistics Sample s X Population  μ Distribution of sample means The standard error is the average amount that you ’ d expect a sample (of size n) to deviate from the population mean –In other words, it is an estimate of the error that you ’ d expect by chance (it is our estimate of the sampling error) Keep your distributions straight by taking care with your notation Properties of the distribution of sample means

20. Reasoning in Psychology Using Statistics Testing Hypotheses –Step 1: State your hypotheses –Step 2: Set your decision criteria –Step 3: Collect your data from your sample –Step 4: Compute your test statistics –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program

21. Reasoning in Psychology Using Statistics Statistical test decision tree Start here How do we know which test to use? –The design of the research: how many groups, how many scores per person, etc.

22. Reasoning in Psychology Using Statistics Generic statistical test Could be difference between a sample and a population, or between different samples Based on standard error or an estimate of the standard error How do we know which test to use? –The design of the research: how many groups, how many scores per person, etc. Both of these parts change as a function of the design As a result, the test statistic changes

23. Reasoning in Psychology Using Statistics Using the distribution of sample means Transform the distribution of sample means into the appropriate standardized distribution (as determined by the design features) Test statistic distribution Test statistic Distribution of sample means We will use 2: z’s & t’s

24. Reasoning in Psychology Using Statistics Same as before,with two differences: –Uses the distribution of sample means –Ask questions about samples rather than individual scores One sample z-test statistic New z-formulaOld z-formula

25. Reasoning in Psychology Using Statistics One sample z-test statistic Old z-formulaNew z-formula raw score sample mean population standard deviation standard error population mean mean of the distribution of sample means

26. Reasoning in Psychology Using Statistics Same as before,with two differences: –Uses the distribution of sample means –Ask questions about samples rather than individual scores One sample z-test statistic New z-formulaOld z-formula

27. Reasoning in Psychology Using Statistics What is the probability of getting a sample of n = 4 students with an average of 630 or better on the SAT? New z-formula What is the probability of getting a 630 or better on the SAT? Old z-formula From the table: z(2.6) =.0047 So the probability is 0.0047 μ = 500, σ = 100, Normal From the table: z(1.3) =.0968 So the probability is 0.0968 μ = 500, σ = 100, Normal One sample z-test statistic

28. Reasoning in Psychology Using Statistics Testing Hypotheses –Step 1: State your hypotheses –Step 2: Set your decision criteria –Step 3: Collect your data from your sample –Step 4: Compute your test statistics –Step 5: Make a decision about your null hypothesis Hypothesis testing: a five step program

29. Reasoning in Psychology Using Statistics Performing your statistical test What are we doing when we test the hypotheses? –Consider a variation of our memory experiment example Population of memory patients MemoryTest μ &  known Memory treatment Memory patients Memory Test X Compare these two means Conclusions: The memory treatment sample are the same as those in the population of memory patients. They aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: We test this one

30. Reasoning in Psychology Using Statistics Performing your statistical test H 0 : is true (no treatment effect)H 0 : is false (is a treatment effect) Two populations One population What are we doing when we test the hypotheses? Real world (‘truth’) XAXA They aren ’ t the same as those in the population of memory patients XAXA The memory treatment sample are the same as those in the population of memory patients. We test this one

31. Reasoning in Psychology Using Statistics “ Generic ” statistical test The generic test statistic distribution (a transformation of the distribution of sample means) –To reject the H 0, you want a computed test statistics that is large The probability of having a sample with that mean is very low –What ’ s large enough? The alpha level gives us the decision criterion Distribution of the test statistic α-level determines where these boundaries go

32. Reasoning in Psychology Using Statistics “ Generic ” statistical test If test statistic is here Reject H 0 If test statistic is here Fail to reject H 0 Distribution of the test statistic The generic test statistic distribution (a transformation of the distribution of sample means) –To reject the H 0, you want a computed test statistics that is large The probability of having a sample with that mean is very low –What ’ s large enough? The alpha level gives us the decision criterion

33. Reasoning in Psychology Using Statistics “ Generic ” statistical test Reject H 0 Fail to reject H 0 The alpha level gives us the decision criterion Two -tailed  = 0.05 0.025 split up into the two tails Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tails. z.00.01….06 -3.4 -3.3 : -1.9 : 0 : 1.0 : 1.9 : 3.4 0.0003 0.0005 : 0.0287 : 0.5000 : 0.8413 : 0.9713 : 0.9997 0.0003 0.0005 : 0.0281 : 0.5040 : 0.8438 :.9719 : 0.9997 ………….0250.9750 Z critical = ±1.96

34. Reasoning in Psychology Using Statistics “ Generic ” statistical test Reject H 0 Fail to reject H 0 The alpha level gives us the decision criterion One -tailedTwo -tailed Reject H 0 Fail to reject H 0 Reject H 0 Fail to reject H 0  = 0.05 0.05 all of it in one tail Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tail. Z critical = +1.645

35. Reasoning in Psychology Using Statistics “ Generic ” statistical test Reject H 0 Fail to reject H 0 The alpha level gives us the decision criterion One -tailedTwo -tailed Reject H 0 Fail to reject H 0 Reject H 0 Fail to reject H 0  = 0.05 0.05 all of it in one tail Go to the table (unit normal table for z-test) and find the z that has 0.050 in the tail. Z critical = -1.645

36. Reasoning in Psychology Using Statistics 1-sample z-test Population of memory patients Memory Test σ is known μ is known Memory treatment Memory patients Memory Test X Compare these two means Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05.

37. Reasoning in Psychology Using Statistics 1-sample z-test Population of memory patients Memory Test σ is known μ is known Memory treatment Memory patients Memory Test X Compare these two means Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. –1 sample

38. Reasoning in Psychology Using Statistics 1-sample z-test Population of memory patients Memory Test σ is known μ is known Memory treatment Memory patients Memory Test X Compare these two means Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. –1 sample –1 score per subject

39. Reasoning in Psychology Using Statistics 1-sample z-test Population of memory patients Memory Test σ is known μ is known Memory treatment Memory patients Memory Test X Compare these two means Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. –1 sample –1 score per subject –Population mean (μ) and standard deviation (σ) are known (assume Normal dist) 1-sample z-test

40. Reasoning in Psychology Using Statistics Performing your statistical test Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using  = 0.05. H0:H0: the memory treatment sample are the same as those in the population of memory patients (or even worse). HA:HA: the memory treatment sample perform better (fewer errors) than those in the population of memory patients μ Treatment > μ pop = 60 μ Treatment < μ pop = 60 One -tailed Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis

41. Reasoning in Psychology Using Statistics Performing your statistical test Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages μ = 60 errors, with σ = 8). Test using α = 0.05. H0:H0: μ Treatment > μ pop = 60 HA:HA: μ Treatment < μ pop = 60 One -tailed Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis  = 0.05

42. Reasoning in Psychology Using Statistics Performing your statistical test Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. H0:H0: μ Treatment > μ pop = 60 HA:HA: μ Treatment < μ pop = 60 One -tailed  = 0.05 n = 16, X = 55 Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis

43. Reasoning in Psychology Using Statistics Performing your statistical test Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. H0:H0: μ Treatment > μ pop = 60 HA:HA: μ Treatment < μ pop = 60 One -tailed  = 0.05 n = 16, X = 55 Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis = -2.5

44. Reasoning in Psychology Using Statistics Performing your statistical test Dr. Mnemonic develops a new treatment for patients with a memory disorder. He hypothesizes that the treatment will improve memory performance. To test it he collects a sample of 16 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors (while the typical memory patient averages 60 errors, with a σ = 8). Test using α = 0.05. Step 1: State your hypotheses H0:H0: μ Treatment > μ pop = 60 HA:HA: μ Treatment < μ pop = 60 One -tailed Step 2: Set your decision criteria  = 0.05 Step 3: Collect your data n = 16, X = 55 Step 4: Compute your test statistics = -2.5 Step 5: Make a decision about your null hypothesis 5% Reject H 0 - Support for our H A, the evidence suggests that the treatment decreases the number of memory errors

45. Reasoning in Psychology Using Statistics Performing your statistical test If time allows: The following pages give examples of situations that require different statistical tests.

46. Reasoning in Psychology Using Statistics Performing your statistical test Population of memory patients MemoryTest  is NOT known  is known Memory treatment Memory patients Memory Test X Compare these two means Hypotheses: the memory treatment sample are the same as those in the population of memory patients. they aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors).

47. Reasoning in Psychology Using Statistics Performing your statistical test Population of memory patients MemoryTest  is NOT known  is known Memory treatment Memory patients Memory Test X Compare these two means Hypotheses: the memory treatment sample are the same as those in the population of memory patients. they aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). –1 sample

48. Reasoning in Psychology Using Statistics Performing your statistical test Population of memory patients MemoryTest  is NOT known  is known Memory treatment Memory patients Memory Test X Compare these two means Hypotheses: the memory treatment sample are the same as those in the population of memory patients. they aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). –1 sample –One score per subject

49. Reasoning in Psychology Using Statistics Performing your statistical test Population of memory patients MemoryTest  is NOT known  is known Memory treatment Memory patients Memory Test X Compare these two means Hypotheses: the memory treatment sample are the same as those in the population of memory patients. they aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). –1 sample –One score per subject –Population mean (μ) is known

50. Reasoning in Psychology Using Statistics Performing your statistical test Population of memory patients MemoryTest  is NOT known  is known Memory treatment Memory patients Memory Test X Compare these two means Hypotheses: the memory treatment sample are the same as those in the population of memory patients. they aren ’ t the same as those in the population of memory patients H0:H0: HA:HA: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Following the treatment he gives them a standard memory test. His sample averaged 55 errors, with a s = 8 (while the typical memory patient averages 60 errors). –1 sample –One score per subject –Population mean (μ) is known –Population standard deviation (  ) is NOT known

51. Reasoning in Psychology Using Statistics Which test do we use? –1 sample –One score per subject –Population mean (  ) is known The single sample t-test can be used when: –Population standard deviation (  ) is NOT known

52. Reasoning in Psychology Using Statistics Performing your statistical test Memory patients Memory performance at the post-test is equal to memory performance at the pre-test. H0:H0: Memory treatment Memory Test X Pre-test Memory Test X Post-test Compare these two means HA:HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Hypotheses: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment.

53. Reasoning in Psychology Using Statistics Performing your statistical test Memory patients Memory performance at the post-test is equal to memory performance at the pre-test. H0:H0: Memory treatment Memory Test X Pre-test Memory Test X Post-test Compare these two means HA:HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Hypotheses: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment. –1 sample

54. Reasoning in Psychology Using Statistics Performing your statistical test Memory patients Memory performance at the post-test is equal to memory performance at the pre-test. H0:H0: Memory treatment Memory Test X Pre-test Memory Test X Post-test Compare these two means HA:HA: Memory performance at the post-test is NOT equal to memory performance at the pre-test Hypotheses: Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and gives them his new treatment. Before the treatment he gives them a pre-treatment memory test and after the treatment a post-treatment memory test. His sample averaged 60 errors before the treatment and 55 errors after the treatment. –1 sample –Two scores per subject

55. Reasoning in Psychology Using Statistics Which test do we use? The related sample t- test can be used when: –1 sample –Two scores per subject

56. Reasoning in Psychology Using Statistics Performing your statistical test Memory patients Memory treatment No Memory treatment related On a pair-by-pair basis every person in the No Treatment group is related to or matched to a person in the Memory Treatment group Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period.

57. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X related Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period.

58. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X related Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period. –2 samples

59. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X related Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he collects a sample of 25 patients and matches them to a sample of similar individuals. He then gives them one sample the new treatment (but not the other). Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his matched sample averaged 60 errors over the same time period. –2 samples –Samples are matched with one score per subject

60. Reasoning in Psychology Using Statistics Which test do we use? –2 samples –Samples are matched with one score per subject The related sample t- test can be used when:

61. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period.

62. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period. –2 samples

63. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period. –2 samples –Samples are independent

64. Reasoning in Psychology Using Statistics Performing your statistical test Memory treatment Memory patients Memory performance by the treatment group is NOT equal to memory performance by the no treatment group. HA:HA: No Memory treatment Memory Test X Memory Test X Compare these two means Hypotheses: H0:H0: Memory performance by the treatment group is equal to memory performance by the no treatment group. Dr. Mnemonic develops a new treatment for patients with a memory disorder. He isn ’ t certain what impact, if any, it will have. To test it he randomly assigns 50 patients to one of two samples. He then gives one sample the new treatment but not the other. Following the treatment period he gives both groups a memory test. His treatment sample averaged 55 errors after the treatment and his control sample averaged 60 errors over the same time period. –2 samples –Samples are independent –One score per subject

65. Reasoning in Psychology Using Statistics Which test do we use? –2 samples The independent sample t- test can be used when: –Samples are independent –One score per subject

66. Reasoning in Psychology Using Statistics Wrap up In lab –Make hypotheses (both null & alternative) –Test hypotheses using 1-sample z-test Questions?