### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Intermediate Educational Statistics EPSY 5381

TTU

GPA 3.99

### View Full Document

## 26

## 0

## Popular in Course

## Popular in Educational Psychology

This 50 page Class Notes was uploaded by Valerie Yundt on Thursday October 22, 2015. The Class Notes belongs to EPSY 5381 at Texas Tech University taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/226398/epsy-5381-texas-tech-university in Educational Psychology at Texas Tech University.

## Similar to EPSY 5381 at TTU

## Reviews for Intermediate Educational Statistics

### 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: 10/22/15

3 C 5 a 2 5M WW 5535 as I 5 m 3 is 53 g L h a J M a p 33 EH9 3ng I xdf ktgw quot quotir p d5 f 5V1 jig ff Fit w 13 Hi 3 fzrq I 2 C L 54 W1 L A A 5 w w i A is 2 0 i 4 77 1 i 3mg WWSRX 5 i 39 f I my It 1 f X J if yaak kvw 5 jggm 473 15 VALVE quot 2 39 Rwy 3 a 2 f 39 z x iv A r w a r g I g W K 53in I 5 x If jg fgw 53 f j x 5 Q X wagi i EJgitgj LC VPN m i K F MC mN am 2 3 7 f4 4 M f irra fa 5 g raw L Erg gz if 39i A M if 55 ew x M m W a f vi5 A Q 3 1 5 f 9ny 3 a w f m f 5 RE N g I fquot M 2 C H giddy 11 W M M r x A W W M M M W w W 125 2m 3 35 z fiat 33 yrngx 33363 65x24 i r 75531 MCL39LV SgL 2kg gwi x 33 5 K g 3 m 5 if 523 15quot 0 wawsl qg ng g wax amp a s g H 39 4 Q 3 M SLECaix w 3 1 a e a if q E s g 5 5 f gargit 3 xi d m quot 5 52 away 26 chyij Xma j V A4 SWquot A y a s E 1AC z M f g 17 Mx a szm 9 M g y Q v X gs X a 3 g M E 5 f A L f 5 miss m V E 5 Eff I lg M E M E f MMQWMW Yr r w 5 E g L g g fquot r 71 3 2 i 3 5 C a 3 f 39 E w j 5 523 i a 3 7 X A 3 g s M 4 g E Q g 53 ng gigha 39 g 3 quot1 I r a g4 52 g g a 25 39 135 vi53 gt0 K 3x w XL 7 gtCkrngx g 5 W 2 3 5 airEEC y 13 wig g g v a 39 fl 2 K figs y 5 E w 9545 sf x Wm Ami a r 9 3 My gig LC C if g 12 A 13m i W hi5 ka 2139 amp w KMN 2amp3quot K j i 5 f 5 g z i y X x yquot i i gt 5 4 iii 3 39 f f i5 wk i 55 5 i c 1 4 19 V K 3 5 1quotW x Via 20 f i glk g w 5 W L ff gt 9 kw MW 1 N 0 gm S Ev Qw a 5 N if if i 2 WV 2 a w w 39m lt w M22 I M K y W i S w X is a i f x M 3 V R raw 5 w M g g saw I A 33quot K EC 1 s 1R5 Vw i rmss y gfg cw 9 g Rf f1 1fir 852533 i x X 2 Cf xv f M a r u 5 W 52 2 E f w 3515 5in an 5 1 j V w M w 12 d V A g Q m 2 m i V Ea k 9 mp g 3 ms m E a N Eiig A w 3 9H m M a at m 3 i 33d j 233 lt x g o M y a W x Ea x 2 5 mm M M5 g m A 2 lt M m M 5m 4 f lt9 g k 1 FEW i N xx m 5 gt 3 ya i 5 us a j A Km Q R 3 6 a g f s M an x a a i 5 5 5 f f a E g w 3 2 i 525 X SW 12 x n a w 1 E m V W gt g N 2 r 3 if iii x m 2 8 I V5 L s f w a z g w a a Z 5 g g g 2 L 33w 3h Wu w w is m m i a y i W n w m v ES 55 if 5 x 3 a k I 3 f M y t blow 2 j K 1 Iii 3 V w Mm as i fart a 3 I 4 2 LE1 fax a x k T 92 55V T r Tu K if N 4 a E 1 r r K w 5335 A 5 3 Av A W 3 5 w a z a sh C s f figfsi m a Effigy xix Hui 3 Mix a ffgfk 5 mus 5 g g Mi fn ijik xx f2 r m 5 r ML a E w E a m c 1 33 x 3 4 x U 5 0i 1 33 f v m 556 X E 5uQ Cf lt1 f E f kg VinCOV 05 5 W43 lt9 is 35 m gislii 5 jva R 3 aw 73 k a f v M as bk W Xi WEW K a f 3 i E 2 if amp a i fix 1 iVAm 353 AM a 5541 a i ii iag as g Eia igxiiazx 5 3 3 i r in 615562 if f g3 33 g j a v lt1 r 3139 quot Q m 8 WW its 17 WWW d quot Wmmw NM Mmmh wmw aw t quot3 a gaff53W ampw L f 7 i 5f 5 Sim n 4 m if 3 3 3 3 4 sfquot 3 3 I iii if I 5 Q J VI 1 W E gtw f Cg 256W W i M3MWW quot57 45 FM 93 A gt Midi n Lx39 mfg a 2 E galK quot quot if z a I 5 a f p I I z r yawm 0 lt3 1 5 15633 iii 9 is 2w fig 39 g if WW a f as xix 4 k c 1 is a 2 C 1 C Eliquotx 139 w V y W C 7quot x 9 Q i mquot i m a K x EMS V 4 k i 4 y K 2 A Ki 3 i M 3 w affkf 3 Page a magi xmv r RE 32 quotm WWMMMWW W f M MNXK f x i t r V i s g r 5quot z g z 3 57 f Chapter 14 r r WWWMWWMS Hypothesis Testing KSample Case Analysis of Variance OneWay Classi cation This chapter presents the procedure for testing the hypothesis that K population means are equal where Kgt2 In other words this chapter addresses what to do when the independent variable has more than two levels You would use a t test in the event there were only two levels Problems with Multiple t Tests If there are more than two levels of the independent variable the research could conduct multiple t tests however this is not appropriate The problem with computing multiple independent t tests for comparing K sample means is that as the number of t tests increases the Type I error rate increases The Type I error rate is determined by 1 l itc where on level of signi cance for each separate t test and c number of independent t tests The Variables in ANOVA Independent variable the variable that forms the groupings This variable is categorical Dependent variable the measure on which the groups are being compared This variable is continuous In AN OVA one way classi cation only one independent variable is considered but there can be two three six or theoretically any nite number of levels of the independent variable For example The researcher may be interested in differences in students math scores dependent vari ble based on the amount of tutoring the student received independent variable or treatment There is only one independent variable tutoring but four levels may exist such as 30 minutes of tutoring one hour one and a half hours and two hours Changes in the dependent variable in ANOVA are or are presumed to be the result of changes in the independent variable Concepts Underlying ANOVA The null hypothesis is that the population means from which the K samples are selected are equal Ho unu2u5 ui Ha u at pk for some i k In order to test the null hypothesis this procedure analyzes the variance of the scores on the dependent variable The total variation of the scores is partitioned into two components The variation of the scores Within the K groups and the variation between the group means and the mean of the total group grand mean Small observed differences between the sample means and the grand mean are attributable to sampling uctuation However sizable differences between the group means and the grand mean resulting in a substantial 883 are an indication that the null hypothesis may not be true Two Estimates of the Population Variance In ANOVA the betweengroups and within groups variance estimates are found by dividing 88 and SSw by the degrees of freedom associated with each of these estimates The resulting between groups and within groups variance estimates are commonly called mean squares Testing the Null Hypothesis The computed mean squares are actually statistics and have counterparts in the population called expected mean squares Discussion of expected mean squares relates the analysis to the linear model in ANOVA See page 358 The F Ratio The difference between the two variances can be tested by forming a ratio of variances and using the F distribution as the sampling distribution Assumptions Underlying AN OVA There are three primary assumptions relevant to AN OVA 1 The observations are random and independent samples from the populations 2 The distributions of the populations from which the samples are selected are normal 3 The variances of the distributions in the populations are equal Homogeneity of variance Generally failure to meet these assumptions changes the Type I error rates To assure that the assumptions are met 1 Use random sampling and appropriate sampling techniques 2 Use a goodnessof t test to check the normality assumption 3 Utilize Bartlett s test for homogeneity of variance ANOVA is robust with respect to violations of the assumptions except in the case unequal variances with unequal sample sizes l of A Measure of Association quotg Rejecting the null hypothesis in ANOVA indicates that there are signi cant differences among the sample means a greater difference than would be expected on the basis of chance With larger sample sizes statistically significant ndings may hold little practical signi cance A 3 Omega squared is a measure of the strength of the association between the independent 2 39 and dependent variables in AN OVA Omega squared indicates the proportion of p I 5 x g k S V F A E a 1 x if H y 5 3 NE aquot KKK iv 1 in preparing a planning re port the director of a community continuing education program classi es course requests a s 1 job related 2 consumer related 3 health related 4 recre ational or 5 other Over ve registration periods the following numbers of special requests were received Use one way ANOVA procedures to determine whether or not the registration data suggest differences in overall community interest Use the 05 level of signi cance 39 Course request classi cations 3 2 l 1 2 3 4 5 r 26 1 18 28 23 g 30 2 25 40 30 35 33 20 26 24 29 ll 16 31 25 24 5 11 20 18 22 5 5 5 5 25 Z 90 145 120 140 110 605 180 290 240 280 220 g 146413 1726 4421 2954 4026 2530 39 ik 15657 16200 42050 28800 39200 24200 2T2nk 15045 a Hui l 1 3 14 5 r 39 ii 8 H pi at pk for some 139 k quot WigVa f freedom F 287 A a 2226 b For K l 4 and N K 20 degrees 0 tv 2 L0 c39 ssnz glUfno TzN 15045 l464l 404 mm Mommy we ssW Tr xikz mlnk 1565715045 612 I1l i1 kl I C A ssT 35 quot xi TZN l5657 i4641016 kl il Summary ANOVA Source SS df MS F F 330 287 quot Between 404 4 Wm g 101 5quot Within 612 20 dmom 3060 3 Total 1 01 6 24 ror me results 01 the oneway ANOVA presented in Exercise 1 use the Tukcy method to test tor pairwwe dili erences among the population means at the 05 level of signi cance Al though not rcqu1red for the Tukey or TukeyKramer procedures the means are ranked from low to h1gh 2 2 Xi Xk Q 2 1x 18 2 4 162 it 6 2 243 0815 I 4 28 10 6 4 405 31243 162 9 29 7 5 1 445993quot 283 202 040 Mswn 306075 247 plt05 Forr 5 and dfw 2ch 423 Therefore pl at 1 all other pairwise compariso s are not statistically signi cant 39 Ex 3 a f 8 fl X3 4 A i 41 2 5 RX a Z 281 a 3 Again referring to the data used 1n Exercxses l and 2 periorm the NewmanKeuls procedure to test for pairwise dif gzrences between means fisc 05 as your level of signi cance a 3 2 59 Q Qcv XI 1 xi 2 22 162 295 X 24 2 243 081 358 295 4 28453 10 6 4 405 243 162 396 358 295 2396 11 7 5 1 445 283 202 040223 423 396 358 295 iMSWn 430605 247 plt01 p 75 114 and p at 114 all other pairwise comparisons are not statistically signi cant 5 For 110 data in Exercise 7 oi39Chaptcr l4 perform 1hc TukcyKramcr procedure 10 lost f or pair wise mean di 39crcnccs Set the level of signi cance at 05 Mel10d I II 111 ilk 5 4 6 N 15 x 2500 2900 3600 Sunuuary ANOVA Smut SS 1139 MS F FW Bctwccn 34173 2 17087 707 389 Within 29000 12 2417 Total 63 173 14 XI nk Xi Xk denominator Q J 250 5 39 290 4 4 233 172 X 360 6 1 1 7 21 1 224 521 313 1 1 r denominator MSw i l plt05 Forr 3111111 dfw 12 QCV 377 39 Therefore 11 ti 3 all other pairwise comparisons are not statistically 51 gm cant 7 Assume that in Exercise 6 the drug dosages were measured on a ratio scale and that the drug dosages increase from Group 1 and Group 4 Use orthogonal polynomial contrasts to test for linear quadratic and cubic trends at the 05 level of signi cance Also graph your results Group 1 2 3 4 X 15 12 75 9 n 10 IO 10 10 7 3 Linear 3 i l 3 Quadratic l l l 1 Cubic 1 3 3 1 g b Fl 315112175392 inear quot39 3682a1 L9 10 10 10 10 2252 6878 736 2 F l15 112 17o519 quadratic 39 368 1 LL 1 10 10 10 10 2 4395 1376 1472 F H 1lt1slt312 3gt7s09 cu 1C 368l 9 2 L 10 10 10 10 2 75 7 64 736 chws 4l l for df l 36 c What are your conclusions All three contrasts are signi cant the linear quadratic and cubic trends are all signi cant The researcher would want to describequot all three but concentrate on the cubic trend E15 u 39D 012 E E9 2 6 E 23 6 l L l i 2 3 4 5P5 5363 g D QCWL WW guy6 Maw4 AIS 3 PairJ 7 A f S geeCS GD 6 Vk 5 kw WP 23 0lt 4 a Macwfm tg K lt i lbw Kl zjA 0ltK 4 3 s66 anav vi 7 53 35 gm M Mm 3mm I 1w Vm m F 4 I gSB VV SLQ gs 4 gym T quot 7 32 5 31 532 4 I 39 Modef 356W SOWWi x191 m3 gcgfjm m CL I aESgoLe fola Cm USC AVG MAW39ZQ q JQSSVOG H I st hmK I JzIMS B Gm if Wc W51 I 1 an W57 384 4 4547 W p2 Tbs B ay mm m Q Aodla for dg v 70 1 3 Clbgo 31 f7 pss to P 3 5 ewk Sac booL MIC On 9C0 X 1 R 5dfmcj CorwP Sea m5 d Dara03 s 3 Bay was uvij nimdf v3 4 A q mdc V 7 fradc 5 N 13 L 399ng 72 7903 267230 3750 47 zs MC Us 34 174 7 Mia 6 26 17396 MW an W9 ma a m37gL j WCWS U mugL amp0 WMWC omp ytgms MoiA3jth 5 L4 7 MM f LM QO gamma V7 ll m m Maf M 4m quot IaCC stomJLk 53 3 Z Curcsidaa 3 N m Java lrl 23 E waaw 3 3 1 039 2 6qu TAR C15 2AM M quot 3 1 a x j st cf 33C 6 I K Kb aimed A y f f a c 4 quot 3 My 3 cw M 3 5 6 0mm 4y is W 39 5 gt Dc m jz gq K b z 65 W I 3 C a 39 Q I 3 myng 52357 a 2M 0 16ch 06quot 1 393 4 7V7 7351 2523449 w Zr75 3 i gmguwi 5a W 3 K on 39ggos q 39 39mm 2 I kc aquot A W SSEAJSsldazk K 239 17 if M S x Ex 1 T accagcov QA quoty N 2 SSwM SST 33 33 CE e icgxavgwQm c M Q lt 39 3 W S Q 1 S K m if 6 i233 i Bays3 w 57 W 392739772 y 1 l8 AmmeWw Hkxig c 1 7 56 E 7L f r ma Q 639 53 i2 may 4 lt4 j Q K mimim g C A 7L r 35 g 5 ag S Q 7 4 2 a Q 4 SKQQMJ gag r iiij f i W W h Z I 1 5 g w 9 mame w gig g c 3 ng f 5 am iWCam 1 m i lag 33 twigf Iquot 3 W Ej 6i gg y i CM 036 4w I f 3 if f S V 1 ii quot f EMA w Ga WC S j w cam a f r 66 S Kquot K a x 1 j a amp6 ya aha mitt J x Wng in Ew i gig 35 J 6 aw 47 Wm W de ng V39f quot 39 I E Li q m WWrig ZJWKQL v5 WQ aw f2 5 fa rm 5 EV wgigfc oi altgtalt5 gig of olt W 6 W M M 3 v Rd 3 w O V kaj G03 Qw wsgwampamp w Ait w WV b Eaj gt 6 2 WSSg quot39 1 U mka 239 fix1S W as r g 346 lt35 1 2 M 37 Bif f 433 W M j c a chzyrfii fv 565 mg EM 395 wigL WC 22 f ka eM fr arf W 7 L w N I awash R j 427 W kw 3V quotTx l j Jim V w St fig 7 stch 3 quot quot3 m 3 NM f7xwsz n is W7 as M 1 Cf gm cpvwgS s wag gjlt Tv if C 1 Vt fj T w W gt V 1 v MO W wa V g k m Ca D p 0362 j 75 Gir ktitr 4W 0 Mfww V66 9ch c Lida m C X38 quot fMWWgT V 3 w 4 1 mg m 7 g xES 1 47 W Jff g j WW WM QM w i Q05 23a 34559 gag 3 Talia Lit3 K c 6 lt7 122 SS g i m t rMw 7lt d 759923 3 I Itquot A X 5 Sic G fyi i i oyx Sp 29 3 i Z S L f Z097 Fm Fi Gaga 5 r 5 j G S cXCUZQf V nz Mm 3 2 S W Zf 717 3 3 igf gs quotAH3 33 1 f I M W i C 2 c 3 g y zN w 1 u my K EEK f 3 f w 6 r Ev w H 5 g of 7x 2g w M x 79 1 a a f 9 x 2 z WWMW MWHWWM NWM WW g if x Ki y 4V

### 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 signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "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.