1. Reasoning in Psychology Using Statistics Psychology 138 2013

2. Reasoning in Psychology Using Statistics Describe the typical college student Age hours of sleep per night hours of studying per week pizza consumption μ = ? μ μ μ –If we can ’ t measure the entire population of students, how do we get the population means for these variables?

3. Reasoning in Psychology Using Statistics μ = ? Two kinds of estimation –Point estimates A single score –Interval estimates A range of scores Estimate it based on what we do know –On information from a sample X –If we can ’ t measure the entire population of students, how do we get the population means for these variables? Estimation

4. Reasoning in Psychology Using Statistics Describe the typical college student Age hours of sleep per night hours of studying per week pizza consumption “ 19 yrs ” “ 17 to 21 yrs ” “ 8 hrs ” “ 4 to 10 hrs ” “ 12 hrs ” “ 2 to 21 hrs ” “ 1 per wk ” “ 0 to 8 per wk ” –Interval estimates –Point estimates

5. Reasoning in Psychology Using Statistics Estimation Estimate the number of people attending lecture today “ 50 students ” “ Somewhere between 20 and 80 students ” How confident are you that your estimate is correct? “ Not real confident, maybe 20% ” “ Not real confident, maybe 20% ” “ Fairly confident, maybe 90% ” “ Fairly confident, maybe 90% ”

6. Reasoning in Psychology Using Statistics AdvantageDisadvantage Estimation A single score A range of scores Confidence in the estimate Little confidence in the estimate “ 50 students ” “ Somewhere between 20 and 80 students ” Kinds of estimation Interval estimate Point estimate

7. Reasoning in Psychology Using Statistics Estimation Both kinds of estimates use the same basic procedure –The formula is a variation of the test statistic formulas (we ’ ll start with the z-score) Multiply both sides byDo some adding/subtracting This is what we want to estimate

8. Reasoning in Psychology Using Statistics Estimation Both kinds of estimates use the same basic procedure –The formula is a variation of the test statistic formulas (we ’ ll start with the z-score) 1)It is often the only piece of evidence that we have, so it is our best guess. 2) Most sample means will be pretty close to the population mean, so we have a good chance that our sample mean is close. Why the sample mean?

9. Reasoning in Psychology Using Statistics Estimation Both kinds of estimates use the same basic procedure –The formula is a variation of the test statistic formulas (we ’ ll start with the z-score) 1)A test statistic value (e.g., a z-score) -based on design (z or t) and level of confidence Margin of error 2)The standard error (the difference that you ’ d expect by chance) - Based on sample size (n) and population standard deviation (σ)

10. Reasoning in Psychology Using Statistics z scores Estimation –You begin by making a reasonable estimation of what the z (or t) value should be for your estimate. For a point estimation, you want what? Finding the right test statistic for your estimate transform z (or t) = 0, right in the middle Z = 0 μ = ? Raw scores

11. Reasoning in Psychology Using Statistics Estimation –You begin by making a reasonable estimation of what the z (or t) value should be for your estimate. For a point estimation, you want what? z (or t) = 0, right in the middle Finding the right test statistic (z or t) For an interval, your values will depend on how confident you want to be in your estimate –What do I mean by “ confident ” ? »90% confidence means that 90% of confidence interval estimates of this sample size will include the actual population mean Actual population mean μ 9 out of 10 intervals contain μ

12. Reasoning in Psychology Using Statistics Estimation –You begin by making a reasonable estimation of what the z (or t) value should be for your estimate. For a point estimation, you want what? z (or t) = 0, right in the middle For an interval, your values will depend on how confident you want to be in your estimate –Computing the point estimate or the confidence interval: Finding the right test statistic (z or t) Step 1: Take your “ reasonable ” estimate for your test statistic Step 2: Put it into the formula Step 3: Solve for the unknown population parameter

13. Reasoning in Psychology Using Statistics Estimates with z-scores Make a point estimate of the population mean given a sample with a X = 85, n = 25, and a population σ = 5. So the point estimate is the sample mean sample mean serves as the center z (or t) = 0, right in the middle

14. Reasoning in Psychology Using Statistics Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5. Estimates with z-scores 95% What two z-scores do 95% of the data lie between?

15. Reasoning in Psychology Using Statistics Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5. Estimates with z-scores What two z-scores do 95% of the data lie between? So the 95% confidence interval is: 83.04 to 86.96 95% 2.5% or 85 ± 1.96 From the table: z(1.96) =.0250

16. Reasoning in Psychology Using Statistics Make an interval estimate with 90% confidence of the population mean given a sample with a X = 85, n = 25, and a population σ = 5. Estimates with z-scores What two z-scores do 90% of the data lie between? So the 90% confidence interval is: 83.35 to 86.65 From the table: z(1.65) =.0500 or 85 ± 1.65 5% 90%

17. Reasoning in Psychology Using Statistics Make an interval estimate with 90% confidence of the population mean given a sample with a X = 85, n = 4, and a population σ = 5. Estimates with z-scores What two z-scores do 90% of the data lie between? So the confidence interval is: 80.88 to 89.13 From the table: z(1.65) =.0500 or 85 ± 4.13 5% 90%

18. Reasoning in Psychology Using Statistics Estimation The size of the margin of error related to: –Level of confidence As confidence increases (e.g., 90%-> 95%), the margin of error gets wider (changes the critical test statistic values) –Sample size As n increases, the margin of error gets narrower (changes the standard error)

19. Reasoning in Psychology Using Statistics Estimation in other designs Different Designs: Estimating the mean of the population from one or two samples, but we don ’ t know the σ How do we find this? Use the t-table & your confidence level Two kinds of estimates that use the same basic procedure –The formula is a variation of the test statistic formulas Depends on the design Center/point estimate? Depends on the design (what is being estimated)

20. Reasoning in Psychology Using Statistics Estimates with t-scores Confidence intervals always involve + a margin of error This is similar to a two-tailed test, so in the t-table, always use the “ proportion in two tails ” heading, and select the α-level corresponding to (1 - Confidence level) What is the t crit needed for a 95% confidence interval? 95% 95% in middle 2.5% so two tails with 2.5% in each 2.5%+2.5% = 5% or α = 0.05, so look here

21. Reasoning in Psychology Using Statistics Estimation in other designs Diff. Expected by chance Confidence interval Estimating the difference between the population mean and the sample mean based when the population standard deviation is not known

22. Reasoning in Psychology Using Statistics Make an interval estimate with 95% confidence of the population mean given a sample with a X = 85, n = 25, and a sample s = 5. What two critical t- scores do 95% of the data lie between? So the confidence interval is: 82.94 to 87.06 From the table: t crit =+2.064 95% 2.5% or 85 ± 2.064 Estimation in one sample t-design

23. Reasoning in Psychology Using Statistics Estimation in related samples design Confidence interval Diff. Expected by chance Estimating the difference between two population means based on two related samples

24. Reasoning in Psychology Using Statistics Dr. S. Beach reported on the effectiveness of cognitive-behavioral therapy as a treatment for anorexia. He examined 12 patients, weighing each of them before and after the treatment. Estimate the average population weight gain for those undergoing the treatment with 90% confidence. Differences (post treatment - pre treatment weights): 10, 6, 3, 23, 18, 17, 0, 4, 21, 10, -2, 10 Related samples estimation Confidence level 90% CI(90%)= 5.72 to 14.28 Estimation in related samples design

25. Reasoning in Psychology Using Statistics Confidence interval Estimating the difference between two population means based on two independent samples Diff. Expected by chance Estimation in independent samples design

26. Reasoning in Psychology Using Statistics Dr. Mnemonic develops a new treatment for patients with a memory disorder. He randomly assigns 8 patients to one of two samples. He then gives one sample (A) the new treatment but not the other (B) and then tests both groups with a memory test. Estimate the population difference between the two groups with 95% confidence. Independent samples t-test situation CI(95%)= -8.73to 19.73 Confidence level 95% Estimation in independent samples design

27. Reasoning in Psychology Using Statistics Relating estimates to hypothesis tests CI(95%)= -8.73to 19.73 -8.7319.73 Notice that this interval includes zero 0 If we had instead done a hypothesis test with an α = 0.05, what would you expect our conclusion to be? - Fail to reject the H 0 H 0 : “ there is no difference between the groups ”

28. Reasoning in Psychology Using Statistics Estimation Summary DesignEstimation (Estimated) Standard error One sample, σ known One sample, σ unknown Two related samples, σ unknown Two independent samples, σ unknown

29. Reasoning in Psychology Using Statistics In labs Practice computing and interpreting confidence intervals