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# PY 211 Test #3 Study Guide!!! PY 211

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This 8 page Study Guide was uploaded by Allie Newman on Saturday October 31, 2015. The Study Guide belongs to PY 211 at University of Alabama - Tuscaloosa taught by Rebecca Allen in Summer 2015. Since its upload, it has received 62 views. For similar materials see Elem Statistical Methods in Psychlogy at University of Alabama - Tuscaloosa.

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Date Created: 10/31/15

PY 211 Book Notes for Test 3 H Chapters 9 and 10 Chapter 9 Estimated Standard Error 0 An estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unknown variance 0 It is an estimate of the standard error or standard distance that sample means deviate from the value of the population mean stated in the null hypothesis T Statistic Also called t obtained or t observed 0 An inferential statistic used to determine the number of standard deviations in at distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis T Distribution 0 Also called Student s t o A normallike distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution 0 The t distribution has greater variability in the tails because the sample variance is not always equal to the population variance Degrees of Freedom df The degrees of freedom for a t distribution are equal to the degrees of freedom for sample variance for a given sample n 1 0 Each t distribution is associated with speci ed degrees of freedom 0 As sample size increases the degrees of freedom also increases OneSample T Test 0 A statistical procedure used to compare a mean value measured in a sample to a known value in the population 0 It is speci cally used to test hypotheses concerning the mean in a single population with an unknown variance 0 3 Assumptions are when computing the onesample t test 0 Normality We assume that the data in the population being sampled are normally distributed 0 Random Sampling We assume that the data in the population were selected via random sampling 0 Independence Each outcome is independent meaning one outcome does not in uence another 0 The t table lists critical values for t distributions with various degrees of freedom 0 The test statistic for a onesample t test is the difference between the sample mean and population mean stated by the null hypothesis divided by the estimated standard error Wher e the ehteined value What dietrlhutien ie new it mate the pre hebility crf b afnin mean li39illet ie the denemineter el the test etetietle De ere knew the pep uletie variance Are degree ef freeElem required fer thie teelquot i hetdee the teat meeau r lfr het een he inferred frern the tweet The Difl f t anti Sll i llJ fltl EEEWEEH 3 T351quot and ET St t feet r etetletieg e eeltue t etetietiel Je value Nerm a Sample l distrlhutlen tdetehutren Ela d rd 9 Eetime39ted standard errear Tee He The eernpe Marianne eueedrtei eetimete the pepuletlen quoteerienre k We treeeuee the pepeletien eerienee iie hnewn TEE The dEQl EE f freedem fer a E teat all equotit39d3 the the degrees ef freedem fer eemwm ea ajn a mm given eemple n 11 The prebehiility ef elletelnlnag e meeeuretl eemgple euteeme Whether the null hypertheeie eheuld be retained er rejeeted Cohen39s d A measure of effect size in terms of the number of standard deviations that mean scores shift above or below the population mean stated by the null hypothesis The larger the value of estimated Cohen s d the larger the effect in the population The sample standard deviation is used to estimate the population standard deviation in the estimated Cohen s d formula Formula sample mean M population mean u Standard Deviation Proportion of Variance A measure of effect size in terms of the proportion or percent of variability in a dependent variable that can be explained or accounted for by a treatment In hypothesis testing a treatment is any unique characteristic of a sample or any unique way that a researcher treats a sample Proportion of Variance variability explained total variability Calculated using the same formula for onesample and twoindependent sample t tests EtaSquared nquot2 o A measure of proportion of variance that can be expressed in a single formula based on the result of a t test 0 nquot2 tquot2 tquot2 df o Eta squared tends to overestimate the size of an effect in a population OmegaSquared Wquot2 o A measure of proportion of variance helps to correct the overestimate of eta squared By subtracting 1 in numerator o Wquot2 tquot2 1 tquot2 df o Omegasquared can only be computed for a t test when t is greater than or equal to 1 Mean ifferenCe EstimatedCDhEIl S Dewatlon t Proportion of vane T1 mil Independent Samples 0 The selection of participants such that different participants are observed one time in each sample or group TwoIndependent Sample T Tests 0 A statistical procedure used to compare the mean difference between two independent groups 0 This test is speci cally used to test hypotheses concerning the difference between two population means where the variance in one or both populations is unknown 0 4 Assumptions are when computing the twoindependent sample t test 0 Normality We assume that the data in the population being sampled are normally distributed 0 Random Sampling We assume that the data in the population were selected via random sampling 0 Independence Each outcome is independent meaning one outcome does not in uence another 0 Equal Variances We assume that the variances in each population are equal to each other This assumption is usually satis ed when the larger sample variance is not greater than two times the smaller 0 The twoindependent sample t test measures the number of standard deviations in at distribution that a mean difference between two groups deviates from the mean difference stated in the null hypothesis g the Degrees of Freedom for a Test TBLE 98 Computirl 7il Effect Size for the TwoIndependent Sample tTest Similar to oneindependent sample ttest an effective size is computed to determine how big an effect is 0 Three measures of effect size 0 Estimated Cohen39s d Place the difference between two sample means in the numerator and the pooled sample standard deviation in the denominator M M d 1 2 Pp 1ls2 The pooled sample standard deviation p is the square root of the pooled sample variance l 2 o EtaSquared proportion of variance l n 2 E n 12 df 2 o OmegaSquared proportion of variance l D 02 E 1 l2 07 APA in Focus Reporting the tStatistic and Effect Size 0 When reporting results of a ttest you must include o The value for the test statistic 0 Degrees of freedom 0 pvalue In addition a gure or table is often used to summarize the means and standard error or standard deviations Cohen s dis most often reported with ttests Estimated Standard Error for the Difference An estimate of the standard deviation of a sampling distribution of mean differences between two sample means Sm1 m2 o It is an estimate of the standard error or standard distance that mean differences can be expected to deviate from the mean difference stated in the null hypothesis Pooled Sample Variance The mean sample variance of two samples 0 When the sample size is unequal the variance in each group or sample is weighted by its respective degrees of freedom only when they are unequal if equal then no need to weight them 0 The larger n is the better the estimate of sample variance will be Pooled Sample Standard Deviation The combined sample standard deviation of two groups or samples o It is computed by taking the square root of the pooled sample variance l square root of squot2 p o This measure estimates the standard deviation for the difference between two population means 0 The pool sample standard deviation is used as an unbiased estimate for the standard deviation of the difference between two population means in the formula for estimated Cohen s d Chapter 1 0 Related Sample 0 Also called dependent sample where participants are related 0 Participants can be related in one of two ways 0 They are observed in more than one group Repeatedmeasures design 0 They are matched experimentally or naturally based on common characteristics or traits Matchedpairs design RepeatedMeasures Design 0 A research design in which the same participants are observed in each treatment a Two types of repeatedmeasures designs are 0 PrePost Design A type of repeatedmeasures design in which researchers measure a dependent variable for participants before pre and after post a treatment 0 WithinSubjects Design A type of repeatedmeasures design in which researchers observe the same participants across many treatments but not necessarily before and after a treatment MatchedPairs Design 0 Also called the matchedsubjects design or the matchedsamples design 0 A research design in which participants are selected and then matched experimentally or naturally based on common characteristics Repeatedl MEESLHF EE Design v Pra iF39oat Design Matched19mm E lgn See WithinSubjects H1 RelatedSamples T Test A statistical procedure used to test hypotheses concerning two related samples selected from population in which the variance in one or both populations is unknown The relatedsamples t test is different from the twoindependent sample t test in that rst we subtract one score in each pair from the other to obtain the difference score for each participant o A difference score is a score or value obtained by subtracting one score from another 0 ln relatedsamples t test difference scores are obtained prior to computing the test statistic There are 2 assumptions to make when computing the relatedsamples t test 0 Normality We assume that the data in the population being sampled are normally distributed 0 Independence Within Groups The samples are related or matched between groups The degrees of freedom for the relatedsamples t test equal the number of difference scores minus 1 0 df nd 1 same treatment in Leaeh group l n This is a Source of errortitle EE WEEH PEFEWE Er39r r39 Pri i i i ii nt differences are not 39IJE39 to having I WHE39F39EEE mm between 39 different gmupag tiar39liepants Furemmpie Pareun Ir a lincrea i i p i i lirem Ef up tit Gimp Ea add Person E El 3 i E increased 3 points This is nail mnsia rent Gitrange and is E 339 Earwie mupg Iha39eiura a mutant pf Birgit the V itcunmsieni i ifieren es am mi ilk 3 WE w i the tins in having different groups if Staft39 t39 m dEtarmine whether this differan e is ahai its L jHt Lila 13 hm 39 it H3puthetieai Set bf ata of qur Paltibipanm WithinGum Error Diferences neeur within eaeh grout Eif though all participants expoedema the Emma aigniiieant This is the difiaranee we are ii iierested in heating W i39if l lacea where di mng an Emmi M133 dli er n es the betweEhgmupa E EE are the difiemripes we are tagsting The other wete Maire di39fiemngeg 353m r r g m a3 9mm in glam they have r39l thif lg to do With hamng different troupe Error For a t test the term error refers to any unexplained difference that cannot be attributed to or caused by having different treatments The standard error of the mean is used to measure the error or unexplained differences in a statistical design Computing difference scores prior to computing the test statistic reduces error by eliminating one possible source of error thereby increasing the power of a hypothesis test Estimated Standard Error for Difference Scores Smd An estimate of the standard deviation of a sampling distribution of mean difference scores It is an estimate of the standard error or standard distance that the mean difference scores deviate from the mean difference score stated in the null hypothesis Random Information To Know The null and alternative hypotheses make statements about a population of mean difference scores The mean difference and the estimated standard error for difference scores are entered in the formula for a relatedsamples t test The relatedsamples t test is computed in the same way for a repeatedmeasures design and a matchedpairs design The standard deviation of difference scores is used to estimate the population standard deviation in the formula for Cohen s d Proportion of variance is computed in the same way for all t tests Measuring Effect Size for RelatedSamples T Test 0 There are 3 measures of effect size for the relatedsamples t test 0 Estimated Cohen39s d To compute estimated Cohen s d with two related samples place the mean difference between the two samples in the numerator and the standard deviation of the difference scores to estimate the population standard deviation in the denominator d Md sD 0 Two Measures of Proportion of Variance EtaSquared OmegaSquared Advantages for Selecting Related Samples 0 Selecting related samples can be more practical Selecting related samples reduces standard error 0 Selecting related samples increases power Homework for Chapter 9 Concept and application problems 11 12 16 18 20 21 amp 24 Problems in research 28 amp 32 Homework for Chapter 10 Conceptual and Application Problems 13 14 20 22 Problems in Research 28 29 30 32

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