### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Exam 2 notes PSYC 210

KU

GPA 3.61

### View Full Document

## 61

## 1

1 review

## Popular in Statistics in Psychological Research

## Popular in Psychlogy

This 14 page Bundle was uploaded by Jill Hinman on Monday February 9, 2015. The Bundle belongs to PSYC 210 at Kansas taught by John Sakaluk in Fall. Since its upload, it has received 61 views. For similar materials see Statistics in Psychological Research in Psychlogy at Kansas.

## Reviews for Exam 2 notes

I'm really struggling in class and this study guide was freaking crucial. Really needed help, and Jill delivered. Shoutout Jill, I won't forget!

-*Marty Abshire*

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/09/15

EXAM 2 09232013 NORMAL CURVE Bellshaped Unimodal Symmetrical Ubiquitous curve shows up everywhere 0 Representative sample are more likely to show the curve 0 So consistent can be used to catch cheaters Eg Chicago school teachers French soldiers height 0 Normal distribution 0 Sample size 0 mean 0 standard deviationsquared 0 much of inferential statistics is built on the assumption that the data are normally distributed 0 the larger the sample the better it represents the population STANDARDIZATION What if we want to compare variables tat are on different scales 0 Height inches vs weight lbs 0 We need a method to convert the raw scores of inches and lbs onto the same standard scale Standardization converts raw scores into standard scores for which we know the percentiles 0 We will convert raw scores into 2 scores 0 Z scores follow a Zdistribution o It is also a normal distribution Zscores can be used to calculate percentiles 0 Given a certain z score what percentile is this observation in Theoretically 100 of the population is represented under the normal curve 0 midpoint is the 50th percentile 2 distribution and percentiles o 68 within 1 SD of the mean 0 96 within 2 SD s 0 gt99 within 3 SD s Z SCORES To compute a z score we need to know the population mean and standard deviation 0 Z scores can be positive or negative 0 Positive above the mean 0 Negative below the mean 0 Z scores are scaled in terms of standard deviation 0 Eg z 078 means you are 78 standard deviation above the mean Ex Hours slept by students on Thursday night 0 population mean 7 0 SD 15 What are Z scores for Z1 5715 133 Z2 9715 133 CONVERT Z SCORES TO RAW SCORES Population mean 53 SD 20 o What are the raw scores X for Z 215 l 2152 53 1 Z 135 l 1352 53 8 Z 85 Z 040 COMPARISONS USING Z SCORES Because we have placed raw scores on a standard scale we can now make comparisons between scores 0 Ex 2008 Michael Phelps vs 1972 Mark Spitz 2008 Phelps had 8 Gold Medals 1972 Spitz had 7 Gold Medals 0 the two swam many of the same events using raw scores you can compare them ZSpitz 11278 12033456 166 ZPhelps 102961094318 203 CENTRAL LIMIT THEOREM 0 States a distribution of sample means is a more normal distribution than a distribution of scores even when the population is not normal 0 Distribution of sample means approaches normality as sample size increases 0 Even when the population is normally distributed 0 Distributions of around 30 sample means are large enough 0 Distribution of means is less variable than a distribution of raw scores 0 Limits the effects of outliers o Is a more precise estimate of the population mean Ex heights in inches of 30 college students from a statistics class Distribution of scores 0 Randomly select students and plot their heights Distribution of means Randomly select 3 students and plot the mean of their heights STANDARD ERROR o a distribution of scores is characterized by population mean u population standard deviation 0 o a distribution of means is characterized by W mean of all possible samples of a given size from a population of individual scores o M standard error of mean a standard deviation of a distribution of means 0 mean of the raw scores is the same as the mean of averages O39M 0 65 6 N1O N 200 GM 5M DISTRIBUTION OF MEANS 0 Can calculate zscores for the means of the distribution of SUMMARY 0 means Zstatistics Tells us how many standard errors a sample mean is from the population mean Ch 7 MuM OM Z The normal curve In uence of sample size Standardization Why Raw scores z scores Z raw scores Making comparisons across scales Central limit theorem Standard errors THE Z TABLE 0 A table of scores with 2 values and the given percentages Not values are only present for positive 2 cores 0 Recall percentile rank is the percentage of score below the observed score USING THE Z TABLE 0 Positive 2 scores 0 To nd the percentile of a positive score nd the percentage between the score and the mean and add 50 0 Negative 2 scores 0 To nd the percentile of a negative 2 score nd the percent beyond the score ie the tail of the distribution 0 to nd above the negative score nd the percentage between the score and the mean and add 50 0 at least as extreme o to nd the percentage more extreme in either direction nd the percentage beyond the score and multiply it by 2 this tells us the percentage of scores that are least as extreme as a given 2 score ex before working out percentages it helps to draw a normal curve what is the percentile for a zscore of 123 o 390750 8907 what is the percentage beyond a zscore of 123 0 1093 what percentage of scores are more extreme 123 o 10932 2186 for an IQ test p 1000 15 Fred has an IQ of 105 what percentile is Fred in ZFred X p O 105100 115 33 ile Fred 1295 50 6223 what percent of individuals have lQ s higher than Fred 3707 What percent of individuals have scores at least extreme as Fred 37072 7414 suppose the average US female height u 645 in o 25 in how tail is a female in the 68th percentile X z o p X z 25 645 6568 47 25 645 found 2 score by 6850 and then looking at mean to z for 18 then using that z score How tail is a female in the 25th percentile because its negative percentile under 50 looking for in tail 6283 67 25 645 Z TABLE AND DISTRIBTION OF MEANS 0 Typically we are interested in samples instead of individuals 0 We can use the mean of our sample and compare it to the population mean 0 This is known as 2 test compares samples to population Assumptions a characteristics we ideally require the population from which we are sampling to have so that we can make accurate inferences o Parametric test inferential stats based on set of assumption about population what well do in this course 0 Nonparametric test inferential stats based on less assumptions about the population beyond this course A statistic is robust if produces a fairly accurate result eve when the data suggests that the population might not meet some of the requirements 3 ASSUMPTIONS 1 the DV is asses using a continuous eg scale measure 0 interval and ratio 2 participants are randomly selected 3 distribution of the population of interest is approximately normal HYPOTHESIS TESTING STEP 1 0 Identity populations distributions and assumptions for test to be used 0 Check that its okay to proceed with the planned hypothesis test 0 check PowerPoint slide for more info 0 STEP 2 0 State the null and research hypotheses Both hypotheses are about the population we are trying to generalize too and not the sample collected 0 Null hypothesis Ho No changeno difference 0 Research hypothesis H1 changedifference STEP 3 0 Determine the characteristics of the comparison distribution What parameters and statistics have to be know in our data set in order to complete the hypothesis test 0 Z test Mean of means standard error Basically computing a 2 statistic STEP 4 0 Determine critical values or cutoffs Decide before running any tests what scores will constitute a signi cant difference between our populations 0 Critical values the test statistic values beyond which we will reject the null hypothesis 0 Critical region area under the distribution curve in which if the test statistic falls we will reject the null hypothesis Also known as alpha 0 Common practice is to set a 05 means that we are going to reject the null if the z stat we calculate is equal or greater than 5 of data 0 Corresponds to the set of scores in the 2 distribution that are higher then that value we would reject our null hypothesis if we got a 2 statistic if there were fewer than 5 of that cut off point 0 196 two tailed test 0 164 one tailed test STEP 5 0 Calculate the test statistic Use the information from step 3 to nd the value of our STEP 6 0 Make a decision Compare your test statistic to the critical values determined in step 4 Decide if you should reject or fail to reject the null hypothesis based on the location under the distribution curve of your test statistic o Statistically signi cant pattern in the data differs from what we would expect by chance Reject the null hypothesis ZTEST EXAMPLE DATA 0 Consideration of Future Consequence CFC Scale 0 How able are you to look ahead and acknowledge the impact of the decision you are making now 0 From a national database of incoming college freshmen 0 Population distribution u 351 o 61 0 We allow students to volunteer and be in a career discussion group and then measure them with the VFV 0 Career discussion group N 45 mean 37 0 Does this discussion group differ from the population on the CFC Step 1 0 Identify populations distributions and assumptions for test to be used 0 Comparison pop national database 0 Pop Of interests career discussion group 0 Distribution 2 dist Of means Step 2 Assumptions 0 Continuous DV Yes scores on the CFC scale 0 Random selection Students elect to take career discussion course 0 Normal distribution Sample size of 45 Step 2 0 State the null and research hypothesis Null there will be no difference between the CFC scores from the quotcareer discussionquot group and the national database 0 Null statistically looks like u pm 0 Research there will be a difference between the CFC scores from the quotcareer discussionquot group and the national database 0 Research statistically looks like u NOT um Step 3 0 Determine the characteristics of the comparison of the comparison distribution dist Of means 0 Need the population parameters u 351 o 61 0 Need distribution of means statistics um 351 om osq Root N 61 sq Root 45 09 Step 4 0 Determine critical values or cutoffs 0 Use alpha 05 0 We have a twotailed hypothesis no direction so well use the extreme 25 of space under both tails o This will equate to zscores at the 25 and 975 percentiles o bc its twotailed zcrit196 alpha 05 o onetailed test hypothesis test in which the research hypothesis is direction positioning either a decrease of an increase in the DV but not both as a result of the IV 0 two hypothesis test in which the research hypothesis does not indicate a direction of difference Step 5 0 Calculate the test statistic 0 Calculate the zscore for the sample mean within a distribution of means zstatistic o 2 37 35109 211 Step 6 0 Make decision 0 211 is higher than the zcrit so we reject the null p lt 05 o the focus group has a higher mean than the gen population does CONFIDENCE INTERVALS Cl Interval estimates Calculating Cl s with z distributions EFFECT SIZE 0 Effect of sample size on statistical signi cance o What effect size is Cohen s d STATISTICAL POWER 0 Five factors that affect statistical power 0 Importance of statistical power GENDER DIFFERENCES IN MATH Some studies have shown gender differences in mathematicssexuaitysefesteemetc o they rejected their null hypothesis 0 when we conduct a hypothesis test we only have two outcomes 0 reject o fail to reject an accurate understanding of gender differences may not be found in significant effects 0 each distribution has variability each distribution has overlap Hyde Fennema amp Lamon 1990 Conducted a metraanalvsis the statistical analysis of a collection of results from individual studies for the purpose of integrating ndings Concluded 0 Mean gender differences in mathematical reasoning were very small 0 When extreme tails of the distribution were removed differences were smaller and reversed direction favored girls 0 The gender differences depended on task Females were better with computation Males were better with problem solving 0 gender difference in mathematics performance very similar ovenap HYPOTHESIS TESTING Statistically signi cant does not always mean quotvery importantquot 0 There is a real measurable difference says nothing about the size or reliability of the difference 0 Knowing two means differ is only part of the story 0 We also should know how much two distributions overlap 0 Notice how much men and women overleaped on the mathematics performance 0 Testing whether one number that s supposed to characterized a population parameter is different from population parameter we are comparing it against 0 quotAre these two the samequot hypothesis testing provides us with a point estimate 0 may want interval estimate 0 real life election polls Mitt Romney will get 51 of votes give or take 3 CONFIDENCE INTERVAL CI 0 Con dence interval interval estimate we would expect for a sample statistic a certain percentage of the time if we were able to sample repeatedly for ztests well create a con dence interval for the sample mean Mower 39 20M Msampe Mupper 20M Msampe o 2 critical value 0 0M standard error measure of precision smaller the oMthe smaller the interval EX Does posting calories on the menu at Starbucks reduce the amount of calories a customer consumer o u247o201 Sampled 1000 people who were provided a menu with calories listen M 232 o The calorie group was signi cantly lower than the Starbuck s population 2 236 Compared to 196 it is a big difference 196 Responds to alpha at 05 o What is the 95 con dence interval calories consumed by sample of participants given menus with calories listed Step 1 lt7 d7 0 O W o

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.