Reasoning in Psychology Using Statistics Psychology 138 2018

Reasoning in Psychology Using Statistics Psychology 138 2018

• Quiz 10, due Friday May 4 th. You may take it up to 10 times, your top score is what counts. • Final Projects Due May 2 nd • Uploaded to Reggie. Net • Lab Exam 4 is Wednesday May 2 nd in lab sections • Final Exam: In here, Wednesday May 9 th 1 -3 PM Reasoning in Psychology Using Statistics

• Inferential Statistics: Procedures which allow us to make claims about the population based on sample data – Hypothesis testing – Testing claims about populations (based on data collected from samples) • Correlation • Regression • Chi-squared test – Estimation – Using sample statistics to estimate the population parameters • Point estimates • Confidence intervals – – 1 -sample z test 1 -sample t test Related samples t-test Independent samples t-test Lab Exam 4: Conclusions from Data Reasoning in Psychology Using Statistics

• Analyze the question/problem. – The design of the research: how many groups, how many scores person, is the population σ known, etc. – Write out what information is given – Is it asking you to test a difference, test a relationship, or make an estimate? – What is your critical value of your test statistic (z or t from table, you’ll need your α-level) • Now you are ready to do some computations – Write out all of the formulas that you will need – Then fill in the numbers as you know them • Interpret your final answer – Reject or fail to reject the null hypothesis? What does that mean? – State your confidence interval and what it means Performing your inferential statistics Reasoning in Psychology Using Statistics

• The design determines the test Which test do I use? Reasoning in Psychology Using Statistics

X Y A 6 6 B 1 2 C 5 6 D 3 4 E 3 2 Suppose that you notice that the more you study for an exam (X= hours of study), the better your exam score typically is (Y = exam score). Test if there is a significant correlation between the two variables (α = 0. 05) Correlation SSY = 16. 0 SSX = 15. 20 SP = 14. 0 Y 6 5 34 2 1 1 2 3 X 4 5 6 2 -tailed H 0 : ρ = 0 HA : ρ ≠ 0 df = n - 2 = 5 - 2 =3 rcrit = 0. 878 Reject H 0 There is a significant positive correlation between study time and exam performance Correlation within hypothesis testing Reasoning in Psychology Using Statistics

• The design determines the test Which test do I use? Reasoning in Psychology Using Statistics

• The “best fitting line” is the one that minimizes the differences (error or residuals) between the predicted scores (the line) and the actual scores (the points) • Directly compute the equation for the best fitting line – Slope Y 6 5 4 3 2 1 1 2 – Intercept • Also need a measure of error: – r 2 (r-squared) – Sum of the squared residuals = SSresidual= SSerror – Standard error of estimate Regression Reasoning in Psychology Using Statistics 3 4 5 6 X

X Y A 6 6 B 1 2 C 5 6 D 3 4 E 3 2 Suppose that you notice that the more you study for an exam (X= hours of study), the better your exam score typically is (Y = exam score). Compute the regression equation predicting exam score with study time. Bi-variate regression SSY = 16. 0 SSX = 15. 20 SP = 14. 0 Hypothesis testing on each of these Y 6 5 34 2 1 r 2 = 0. 806 Prediction with Bi-variate regression Reasoning in Psychology Using Statistics 1 2 3 X 4 5 6

• Measures of Error • SPSS Regression output gives you a lot of stuff • r 2 • Standard error of the estimate • Unstandardized coefficients – “(Constant)” = intercept – Variable name = slope • These t-tests test hypotheses – H 0: Intercept (constant) = 0 – H 0: Slope = 0 Hypothesis testing with Regression Reasoning in Psychology Using Statistics

• The design determines the test Which test do I use? Reasoning in Psychology Using Statistics

• When do we use these methods? – When we have categorical variables Step 1: State the hypotheses and select an alpha level Step 2: Compute your degrees of freedom df = (#Cols-1)*(#Rows-1) & Go to Chi-square statistic table and find the critical value Step 3: Obtain row and column totals and calculate the expected frequencies Step 4: compute the χ2 Step 5: Compare the computed statistic against the critical value and make a decision about your hypotheses Crosstabulation and χ2 Reasoning in Psychology Using Statistics

• Inferential Statistics: Procedures which allow us to make claims about the population based on sample data – Hypothesis testing – Testing claims about populations (based on data collected from samples) • Correlation • Regression • Chi-squared test – Estimation – Using sample statistics to estimate the population parameters • Point estimates • Confidence intervals – – 1 -sample z test 1 -sample t test Related samples t-test Independent samples t-test Lab Exam 4: Conclusions from Data Reasoning in Psychology Using Statistics

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

• Both kinds of estimates use the same basic procedure • Finding the right test statistic (z or t) Margin of error – 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: • 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 Estimation Reasoning in Psychology Using Statistics

• The size of the margin of error related to: – Sample size • As n decreases, the margin of error gets wider(changes the standard error) – Level of confidence • As confidence decreases (e. g. , 95%-> 90%), the margin of error gets narrower (changes the critical test statistic values) Estimation 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. or 85 ± 1. 96 All centered on 85 81 83 85 87 89 83. 04 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. or 85 ± 1. 65 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. or 85 ± 4. 13 Estimates with z-scores Reasoning in Psychology Using Statistics 86. 96 narrower 83. 35 86. 65 wider 80. 88 89. 13

• The design determines the formula that you’ll use for the estimation Which test do I use? Reasoning in Psychology Using Statistics

• The design determines the formula that you’ll use for the estimation Design Estimation One sample, σ known One sample, σ unknown Two related samples, σ unknown Two independent samples, σ unknown Estimation Summary Reasoning in Psychology Using Statistics (Estimated) Standard error

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. What two z-scores do 95% of the data lie between? So the 95% confidence interval is: 83. 04 to 86. 96 or 85 ± 1. 96 From the table: z(1. 96) =. 0250 2. 5% 95% Estimates with z-scores 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 tscores do 95% of the data lie between? From the table: tcrit =+2. 064 So the confidence interval is: 82. 94 to 87. 06 or 85 ± 2. 064 2. 5% 95% Estimation in one sample t-design 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 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 Confidence level 95% CI(95%)= -8. 73 to 19. 73 Estimation in independent samples design Reasoning in Psychology Using Statistics