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Psy 202 Test 2 Study Guide

by: Anna Ballard

Psy 202 Test 2 Study Guide Psy 202

Marketplace > University of Mississippi > Psychology > Psy 202 > Psy 202 Test 2 Study Guide
Anna Ballard
GPA 3.33

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These notes cover what will be on Exam 2 which includes chapters 6-10.
Elementary Statistics
Mervin R Matthew
Study Guide
Psychology, Statistics
50 ?




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This 7 page Study Guide was uploaded by Anna Ballard on Thursday October 6, 2016. The Study Guide belongs to Psy 202 at University of Mississippi taught by Mervin R Matthew in Fall 2016. Since its upload, it has received 66 views. For similar materials see Elementary Statistics in Psychology at University of Mississippi.

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Date Created: 10/06/16
FA16 PSY 202 Section 1 Exam 2 Review Sheet Chapter 6 I. CORRELATION Comparison with regression • Correlation Model – neither variable is dependent on the other; the two can be related but that does not mean one causes the other - Correlation ≠ causation - Lowest possible value for correlation = -1.00 o Means there is a perfect negative correlation  as one variable increases, the other decreases - Highest possible value for a correlation = +1.00 o Means there is a perfect positive correlation  As one variable increases, the other increases - A value of 0 means there is no correlation at all o The closer the value is to 0, whether that value is negative or positive, means the correlation is not as strong • Regression Model – predicts cause and effect between variables - Used for quasi-experimental designs - Uses independent and dependent variables II. SCATTERPLOTS How they’re created - ONLY SCATTERPLOTS show all scores in a distribution o Y-axis and X-axis  Plot each pair of the variables on the graph  Every single pair  This helps with correlation coefficients - Magnitude tells us how strong the correlation between the two variables is o how far away from |1| determines how strong What their shape tells us about the bivariate distribution - Shape tells us the strength of the linear association o Positive vs. negative correlation o If our scatterplot is not linear, the information given to us by the correlation coefficient is underestimated III. INTERPRETING THE CORRELATION COEFFICIENT (PEARSON’S R) Other Considerations - Restrictions in range - Presence of outliers - Presence of subgroups - Causality To use Pearson product-moment correlation our data must be: - continuous and linear - Interval and ratio scales IV. ALTERNATIVE APPROACHES TO CORRELATION Which approaches fall into each subcategory & Characteristics of data for which each is used - Other Product-moment correlation coefficients o Spearman Rank Correlation, Point-Biserial Correlation, and The Phi Coefficient  Still must be continuous and linear with interval and ratio scales - Non-product-moment with quantitative and dichotomous variables o The Biserial Correlation Coefficient and the Tetrachoric Correlation - Non-product-moment for categorical values o Contingency Coefficient and Cramer’s V Chapter 7 I. STATISTICAL EQUATION OF A LINE • Y-hat –> predicted value of Y • b0–> Y-intercept • b1–> slope of the line II. CHOOSING LINE OF BEST FIT Difficulties • We cannot know what line best summarizes a bivariate distribution by just looking at its scatterplot - Because many lines can be found to summarize most scatterplots - Must find the line that does best job of including every score Sum of squared error • Estimation for all data points - Helps predict Y from X and also squares the terms in error of estimation to find the best line possible o Sum of squared errors helps us figure out which line best summarizes a scatterplot  We want a lower sum because this means the line fits the distribution best with least amount of error • Errors of estimation (residuals) - The difference between the predicted scores and the actual scores o Vertical distance between Y an1 Y hat o The amount of variance not shared • Equations that minimize Sum of Squared Errors - Because we have more than one population parameter, we lose 2 degrees of freedom for estimates of 2 means o Deviations taken from regression line which have 2 statistics: X and Y Proportion of variance accounted for • This is how well X predicts Y - Aka how much variance in Y is shared with X - Calculated by dividing the sum of squares between groups by the sum of squares total Reversing the roles of the IV and DV - How relation of one slope predicts the other o Geometric mean Standardized regression solution - How to use the z-score for X to predict the z-score for Y o Predicting Y using X  Y-intercept where X = 0 intersects to where Y = 0  Y intercept always equal to 0  Slope  Slope is always = r xy Standard error of the estimate - Treats error across entire regression line as equal o Why it is not a good predictor for the population - Can also differ in terms of y-intercept and slope Standard error of the prediction • Confidence Interval – to predict the average value of Y at a particular X • Prediction Interval – to predict the individual values of Y at a particular X Cook’s distance (D) • Sometimes one point will pull entire regression line towards it - If D is larger than 1, there is a substantial influence • Cook’s distance tells us whether its pulling the regression line but NOT how it is pulling it Chapter 8 I. THREE VIEWS OF PROBABILITY Definitions of each • Personal/Subjective View - Used most often - Humans are naturally terrible at probability, so this is not the one we should us for statistical inference - Biggest issue: not based on imperical probability o Based on how a person feels, which can change from moment to moment and person-person  Predictions one person might make will be very different than predictions of someone else • Classical/Logical View - How nature distributes events • Empirical/Relative Frequency View - nA–> number of outcomes satisfying condition A - n –> total number of observed outcomes o if you have a large enough sample, the probability that you get from that sample should mimic that of the population from which the sample came from Why the personal/subjective view can’t be used • It is based on how a person feels - Means it can change from moment-moment and person-person How the empirical/relative frequency view and classical/logical view are related • As sample size increases, empirical/relative frequency view should start to converge with the classical/logical view II. DEFINITIONS • Experiment – some probabilistic event you make some predictions based off of and then the observe the outcome to see how solid your predictions were • Event - Simple event – one outcome can satisfy it - Compound event – multiple outcomes could satisfy it • Sample space – how many possible events there are • Probability function – defines the probability that any individual event will occur III. RULES FOR FINDING PROBABILITIES Meanings of terms • P(AB) –> probability of A or B • P(AB) –> probability of A and B When we simplify formulas • Simplify formula only when A and B are mutually exclusive Additive/union rule P(AB) = P(A) + P(B) – P(AB) - Subtract probability of both events happening together to eliminate the probability of anything being counted twice. P(AB) = P(A) + P(B) - If A and B are mutually exclusive, we do not have to subtract that probability Multiplicative/intersection rule P(AB) = P(A)* P(B|A) - Multiply probabilities of each B and A o P(A|B) –> probability of B given A P(AB) = P(A)* P(B) IV. RULES FOR COUNTING • Fundamental counting rule • Permutations – P = nn - n = number of permutations of n objects • Combinations – number of combinations of an object using r < n - combinations do not care about the orders - How they relate to permutations Chapter 9 Probability distributions • Definition - Probability distribution – tells us the probability that the random variable will take on each of its possible values o Classical/logical side of probability • Random variables – variable whose value is determined by probability • Sampling distributions – probability distribution based on repeated samples of a statistic - Empirical/relative frequency side of probability - If you have a large enough sample, sampling distribution should resemble probability distribution because the 2 should converge o like why empirical/relative frequency converges with classical/logical when there is a large enough sample size Bernoulli trials • Five characteristics 1) only 2 possible outcomes o success and failure 2) p + q = 1.00 o probability success –> p o probability failure –> q 3) specified number of trials o how many trials you are going to do 4) those trials have to be independent of each other 5) random variable The binomial expnnsirn (n-r) •P(Y = r) = C p qr - C = # of combinations o C –> 4 coins; 2 land on heads 2 - r –> how many heads you wanted - C =rn! / (4 – 2)!2! = 6 - = 6/16 The binomial distribution • Know how to read a Pascal’s triangle Expected value of a random variable • Definition - Expected Value – measure of central tendency; average for a random value over an infinite set of scores • How it’s calculated - E(Y) = ∑[Y • j(Y )] =jµ y - Get products of the possible values first first and sum them • Relationship to the population mean - µ y mean Variance of a random variable • Use expected value to get variance of infinite set of scores Probability and area • For the binomial distribution • Why it can’t be calculated the same way for continuous distributions - Must figure out area under curve instead Chapter 10 Normal distributions • Characteristics - Bell-curve – shape of distribution o Infinite number of possible values o Frequency polygon that never touches X value - Kurtosis & Skewness both = 0 o Helpful for lots of reasons - 3 major measure of central tendency: mean, median, mode are all equal o What goes on one side must go to the other o 50% above and below median - Points of inflection at -1 and +1 o 34.1% distribution between the mean and that 1  away o mean of unit normal distribution always = 0 and standard deviation always =1 • Reasons for importance - Many values in nature are already normally distributed, certain distributions are pretty close approximations to normal distribution o AKA even if distribution is not normal, you can calculate the normal distribution for the original distribution - All distributions can be connected by deriving info from the formula we use for normal distribution. • Transforming to the unit-normal distribution - Compare to other normal distributions by converting a unit-normal distribution to a normal distribution o mean of 0 o standard deviation of 1 o use the table of probabilities for that normal distribution. • Areas under the curve - Above o Convert the raw scores into Z-scores - Below o Convert the raw scores into Z-scores - Between o Convert Y into z-scores and subtract lowest value from the highest. • Approximating the binomial distribution - Ex: coin flips – 20 flips –> n = 20 - Want percent of distribution higher than 9 o Convert 9 into a z-score after adjusting for continuity  Adjust because these are discrete variables o The more times you flip the coin, the more the distribution becomes normal  More trials –> more normal Sampling distribution of the mean • Definition - Sampling Distribution of the mean – distributes the averages of the raw scores o these averages will create the sampling distribution, which comes out to be approximately normal o based on repeated samples. • Purpose • Central limit theorem - Tells us no matter what the raw score distribution looks like, sample distribution is still going to come out normal o means will still be equal o as sample size gets bigger, standard error of mean gets smaller which means sample means get closer to grand mean  grand mean always equals mean for the raw scores of the population. o hypothetically, if N equals infinite size, standard error would = 0 - Standard error of the mean – quantifies how precise we know the true mean of a population • Three possible explanations for extreme scores 1) Sampling error (can’t really avoid) - took too many of one type in your raw scores just by chance 2) Sampling bias - Sample differs from population due to the way you drew the sample - Did not use simple random sampling (our preferred way) 3) Sample comes from a different population - Worry about the most; key for inferential statistic - “Phantom distributions” around the one we think we get our sample from


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