Reasoning in Psychology Using Statistics Psychology 138 2018

Reasoning in Psychology Using Statistics Psychology 138 2018

• Exam 2 in lecture and lab on Wednesday • Be prepared to do calculations (including square roots) on calculator Announcements Reasoning in Psychology Using Statistics

• We’d like to say: – • X causes Y To be able to do this: 1. The causal variable must come first 2. There must be co-variation between the two variables 3. Need to eliminate plausible alternative explanations Causal claims Reasoning in Psychology Using Statistics

• We’d like to say: – • X causes Y To be able to do this: 1. The causal variable must come first 2. There must be co-variation between the two variables 3. Need to eliminate plausible alternative explanations • Directionality Problem (temporal precedence): – Happy people sleep well - Or sleeping well makes you happy? Causal claims Reasoning in Psychology Using Statistics

• We’d like to say: – • X causes Y To be able to do this: 1. The causal variable must come first 2. There must be co-variation between the two variables 3. Need to eliminate plausible alternative explanations • Third Variable Problem: - Happy people sleep well - Or does sleeping well make you happy? Other • OR something else makes people happy and sleep well! Variable • Regular exercise • Minimal use of drugs & alcohol • Being a conscientious person • Being a good relationship Causal claims Reasoning in Psychology Using Statistics

• We’d like to say: – • X causes Y To be able to do this: 1. The causal variable must come first 2. There must be co-variation between the two variables 3. Need to eliminate plausible alternative explanations • Coincidence (random co-occurence) – r=0. 52 correlation between the number of republicans in US senate and number of sunspots » From Fun with correlations » See also Spurious correlations Causal claims Reasoning in Psychology Using Statistics Correlation is not causation blog posts: Internet’s favorite phrase Why we keep saying it

Descriptive Statistics - Statistical procedures to help organize, summarize & simplify large sets of data 1. One variable (frequency distribution) • Display results in a frequency distribution table & histogram (or bar chart if categorical variable). Make a deviations table to get measures of central tendency (mode, median, mean) & variability (range, standard deviation, variance). • 2. Two variables (bivariate distribution) • • 3. Display results: Make a scatterplot. Make a bivariate deviations or z-table to get Pearson’s r. Z-scores & normal distribution Review for Exam 2: Descriptive statistics Reasoning in Psychology Using Statistics

• Are hours sleeping related to GPA? – You conduct a survey. • Your sample of 10 gives these results for average hours per night sleeping: 7, 6, 7, 8, 8, 7, 9, 5, 9, 6 • You also have respondents give their overall GPA: 2. 4, 3. 9, 3. 5, 2. 8, 3. 0, 2. 1, 3. 9, 2. 9, 3. 6, 2. 7 – We will focus on sleep results first and then both variables together. • What kind of scales are they? • To find standard deviation, will we use formula for population or sample? Example Reasoning in Psychology Using Statistics

Hrs. sleep n=10 7, 6, 7, 8, 8 7, 9, 5, 9, 6 X 9 8 7 f p % cf c% 6 5 ∑ 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

Hrs. sleep n=10 7, 6, 7, 8, 8 7, 9, 5, 9, 6 ∑ X 9 8 7 f 2 2 3 6 5 2 1 10 p % cf c% 1. 0 100 Will enter first two columns as X and Y axes for frequency distribution Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

Hrs. sleep n=10 p = f/n ∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 6 5 2 1 . 2. 1 20 10 10 cf c% 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 6 5 2 1 . 2. 1 20 10 10 cf c% 1 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 cf c% 6 5 2 1 . 2. 1 20 10 3 1 30 10 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 cf c% 6 60 6 5 2 1 . 2. 1 20 10 3 1 30 10 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 cf c% 8 6 80 60 6 5 2 1 . 2. 1 20 10 3 1 30 10 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

∑ X 9 8 7 f 2 2 3 p. 2. 2. 3 % 20 20 30 cf 10 8 6 c% 100 80 60 6 5 2 1 . 2. 1 20 10 3 1 30 10 10 1. 0 100 Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

Hrs. sleep X 9 8 7 f 2 2 3 6 5 2 1 F R E Q U E N C Y 6 5 4 3 2 1 5 6 7 8 9 SCORE Step 1: Frequency distribution & histogram Reasoning in Psychology Using Statistics

• Suppose that you combine two groups together. – How do you compute the new group mean? Group 1 110 110 Group 2 New Group 140 140 A weighted mean Reasoning in Psychology Using Statistics

• Suppose that you combine two groups together. – How do you compute the new group mean? Group 1 110 110 Group 2 New Group 140 140 A weighted mean Reasoning in Psychology Using Statistics Be careful computing the mean of this distribution, remember there are groups here X 9 8 7 f 2 2 3 6 5 2 1 9 9 8 8 7 7 7 6 6 5

Hrs. sleep n = 10 X 9 9 Create table, sorted in descending order 8 8 7 7 7 6 6 5 Step 2: Deviations table Reasoning in Psychology Using Statistics

X Hrs. sleep n = 10 9 9 8 8 7 7 7 6 6 5 ∑ 72 Step 2: Deviations table Reasoning in Psychology Using Statistics Mode = 7 (filled in) Median = 7 (arrow) Mean = (∑X)/n = 72/10 = 7. 2 Range = 5 to 9

X Hrs. sleep n = 10 ∑ 9 1. 8 8 . 8 7 -. 2 6 -1. 2 5 -2. 2 72 7. 2 0 = 9 -7. 2 Step 2: Deviations table Reasoning in Psychology Using Statistics Mode = 7 Median = 7 Mean = (∑X)/n = 72/10 = 7. 2 Range = 5 to 9

X Hrs. sleep n = 10 ∑ 9 1. 8 3. 24 = 1. 82 9 1. 8 3. 24 8 . 8 . 64 7 -. 2 . 04 6 -1. 2 1. 44 5 -2. 2 4. 84 72 7. 2 0 15. 6 = SS Step 2: Deviations table Reasoning in Psychology Using Statistics Mode = 7 Median = 7 Mean = ∑X/n = 72/10 = 7. 2 Range = 5 to 9 SD for sample = √ 15. 6/9 = √ 1. 73 = 1. 32

• The mean • The standard deviation – Change/add/delete a given score, then the mean will change. – Add/subtract a constant to each score, then the mean will change by adding(subtracting) that constant. – Add/subtract a constant to each score, then the standard deviation will NOT change. – Multiply (or divide) each score by a constant, then the mean will change by being multiplied by that constant. – Multiply (or divide) each score by a constant, then the standard deviation will change by being multiplied by that constant. Reasoning in Psychology Using Statistics Characteristics of a mean & standard deviation

Person A B C D E F G H I J Hrs. 7 6 7 8 8 7 9 5 9 6 GPA 2. 4 3. 9 3. 5 2. 8 3. 0 2. 1 3. 9 2. 9 3. 6 2. 7 G P A 4. 0 3. 5 3. 0 2. 5 2. 0 1. 5 1. 0 5 6 7 8 Hours of sleep Step 3: Scatterplot Reasoning in Psychology Using Statistics 9

Person A B C D E F G H I J Hrs. 7 6 7 8 8 7 9 5 9 6 GPA 2. 4 3. 9 3. 5 2. 8 3. 0 2. 1 3. 9 2. 9 3. 6 2. 7 G P A What does shape of envelope indicate about correlation? low positive correlation 4. 0 B 3. 5 3. 0 G C H 2. 5 I DE J 2. 0 A F 1. 5 1. 0 5 6 7 8 Hours of sleep Step 3: Scatterplot Reasoning in Psychology Using Statistics 9

Person A B C D E F G H I J K Hrs. 7 6 7 8 8 7 9 5 9 6 5 GPA 2. 4 3. 9 3. 5 2. 8 3. 0 2. 1 3. 9 2. 9 3. 6 2. 7 1. 0 What does shape of envelope indicate about correlation? moderate positive correlation G P A 4. 0 B 3. 5 3. 0 G C H 2. 5 I DE J 2. 0 A F 1. 5 1. 0 K 5 6 7 8 Hours of sleep Step 3: Scatterplot, Effect of outlier Reasoning in Psychology Using Statistics 9

Person A B C D E F G H I J K Hrs. 7 6 7 8 8 7 9 5 9 6 9 GPA 2. 4 3. 9 3. 5 2. 8 3. 0 2. 1 3. 9 2. 9 3. 6 2. 7 1. 0 What does shape of envelope indicate about correlation? low negative correlation G P A 4. 0 B 3. 5 3. 0 G C H 2. 5 I DE J 2. 0 A F 1. 5 1. 0 K 5 6 7 8 Hours of sleep Step 3: Scatterplot, Effect of outlier Reasoning in Psychology Using Statistics 9

X Y 9 1. 8 3. 24 3. 9 0. 82 0. 67 1. 476 9 1. 8 3. 24 3. 6 0. 52 0. 27 0. 936 8 0. 64 3. 0 -0. 08 0. 01 -0. 064 8 0. 64 2. 8 -0. 28 0. 86 -0. 224 7 -0. 2 0. 40 3. 5 0. 42 0. 18 -0. 084 7 -0. 2 0. 04 2. 4 -0. 68 0. 46 0. 136 7 -0. 2 0. 04 2. 1 -0. 98 0. 96 0. 196 6 -1. 2 1. 44 3. 9 0. 82 0. 67 -0. 984 6 -1. 2 1. 44 2. 7 -0. 38 0. 14 0. 456 5 -2. 2 4. 84 2. 9 -0. 18 0. 03 0. 396 0. 0 15. 6 30. 8 0. 0 3. 47 2. 24 SSX 3. 08 SSY SP Sum 72 Mean 7. 2 Step 4: Bivariate Deviations Table Reasoning in Psychology Using Statistics n=10 Note signs! +r or – r?

XY co-deviations ___2. 24___ = _2. 24_ =. 304 = √ 15. 6 * 3. 47 √ 54. 132 7. 357 X deviations, Y deviations Pearson’s r & summary statistics Reasoning in Psychology Using Statistics

SRA (Scientific Reasoning Assessment) (fictional) • Based on normative data: Normal, μ = 50. 0, σ = 10. 0 • Preparing for your analyses – Write down what you know – Make a sketch of the distribution (make a note: population or sample) 40 μ 60 An example Reasoning in Psychology Using Statistics – – Determine the shape What is best measure of center? What is best measure of variability? Mark the mean (center) and standard deviation on your sketch

SRA (Scientific Reasoning Assessment) (fictional) • Based on normative data: Normal distr. , μ = 50. 0, σ = 10. 0 • Question 1 • If George got a 35 on the SRA, what is his percentile rank? Unit Normal Table 0. 0668 40 -1. 0 m 60 1. 0 • Since a normal distribution, can use Unit Normal Table to infer percentile. That’s 6. 68% at or below this score (definition of percentile) z-scores & Normal Distribution Reasoning in Psychology Using Statistics

SRA (Scientific Reasoning Assessment) (fictional) • Based on normative data: Normal distr. , μ = 50. 0, σ = 10. 0 • Question 2 Unit Normal Table • What proportion of people get between a 40 and 60 on the SRA? 0. 1587 40 -1. 0 m 60 1. 0 That’s about 32% outside these two scores That leaves 68% between these two scores • Since a normal distribution, can use Unit Normal Table to infer percentile. z-scores & Normal Distribution Reasoning in Psychology Using Statistics

SRA (Scientific Reasoning Assessment) (fictional) • Based on normative data: Normal distr. , μ = 50. 0, σ = 10. 0 • Question 3 a transformation • Suppose that Chandra took a different reasoning assessment (the RSE: Based on normative data, Normal distr. , μ= 100, σ = 15). She received a 130 on the RSE. Assuming that they are highly positively correlated, what is the equivalent score on the SRA? z-scores & Normal Distribution Reasoning in Psychology Using Statistics

SRA (Scientific Reasoning Assessment) (fictional) • Based on normative data: Normal distr. , μ = 50. 0, σ = 10. 0 (for RSE) (for SRA) transformation • Question 3 a • Suppose that Chandra took a different reasoning assessment (the RSE: Based on normative data, Normal distr. , μ= 100, σ = 15). She received a 130 on the RSE. Assuming that they are highly positively correlated, what is the equivalent score on the SRA? z-scores & Normal Distribution Reasoning in Psychology Using Statistics

• In lab: continue to review, including SPSS • Questions? Wrap up Reasoning in Psychology Using Statistics