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# PY 211 CH. 9 and 10 Notes! PY 211

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This 5 page Class Notes was uploaded by Allie Newman on Saturday October 31, 2015. The Class Notes belongs to PY 211 at University of Alabama - Tuscaloosa taught by Rebecca Allen in Summer 2015. Since its upload, it has received 31 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 Chapter 9 and 10 Bok Summaries Chapter 9 0 Explain why a tdistribution is associated with n 1 degrees of freedom and describe the information that is conveyed by the tstatistic o The tdistribution is a normallike distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance in order to estimate the standard error in this distribution 0 The tdistribution is a sampling distribution for tstatistic values that are computed using the sample variance to estimate the population variance in the formula As sample size increases the sample variance more closely estimates the population variance The result is that there is less variability in the tails of a tdistribution as the sample size increases Each tdistribution is associated with the same degrees of freedom as sample variance for a given sample df n 1 o The tstatistic is an inferential statistic used to determine the number of standard deviations in a tdistribution that a sample mean deviates from the mean value ort mean difference stated in the null hypothesis 0 Calculate the degrees of freedom for a onesample ttest and a two independent sample ttest and locate critical values in the ttable o The degrees of freedom for a tdistribution are equal to the degrees of freedom for sample variance n 1 As the degrees of freedom increase the tails of the corresponding t distribution change and sample outcomes in the tails become less likely o The degrees of freedom for a onesample ttest are n 1 o The degrees of freedom for a twoindependent sample ttest are n1 1 n2 ii 0 Identify the assumptions for the onesample ttest and compute a one sample ttest and interpret these results 0 We compute a onesample ttest to compare a mean value measured in a sample to a known value in the population It is speci cally used to test hypotheses concerning a single population mean from a population with an unknown variance We make 3 assumptions for this test the onesample t test Normality Random Sampling and Independence o The larger the value of the test statistic the less likely a sample mean would be to occur if the null hypothesis were true and the more likely we are to reject the null hypothesis The test statistic for a onesample t test is the difference between the sample mean and the population mean divided by the estimated standard error M SD SM 2 SM Where J o The estimated standard error is an estimate of the standard deviation of a sampling distribution of sample means 2 It is an estimate of the standard error or standard distance that sample means can be expected to deviate from the value of the population mean stated in the null hypothesis 0 Compute effect size and proportion of variance for a onesample t test 0 Effect size measures the size of an observed difference in a population For the onesample ttest this measure estimates how far or how many standard deviations an effect shifts in a population The formula for estimated Cohen s dfor the onesample ttest is Mu 0 SD 0 Proportion of variance is a measure of effect size in terms of the proportion or percent of variability in a dependent variable that can be explained by a treatment ln hypothesis testing a treatment is considered any unique characteristic of a sample or any unique way that a researcher treats a sample 2 measures of proportion of variance are computed in the same way for allttests t n EtaSquared l 8 07 o Etasquared tends to overestimate proportion of variance explained by treatment 12 1 02 OmegaSquared l t2 aquot o Omegasquared gives a more conservative estimate 0 Identify the assumptions for the twoindependent sample ttests and compute a twoindependent sample ttest and interpret these results 0 We compute a twoindependent sample ttest to compare the mean difference between two groups This test is speci cally used to test hypotheses concerning the difference between two population means from one or two populations with unknown variances 4 assumptions are made for this test the twoindependent sample t test Normality Random Sampling Independence and Equal Variances o The larger the value of the test statistic the less likely a sample mean would be to occur if the null hypothesis were true and the more likely we are to reject the null hypothesis The test statistic for a twoindependent sample t test is the mean difference between two samples minus the mean difference stated in the null hypothesis divided by the estimated standard error for the difference o The estimated standard error for the difference is an estimate of the standard deviation of a sampling distribution of a mean differences between two samples It is an estimate of the standard error or distance that mean differences can deviate from the mean difference stated in the null hypothesis 0 Compute effect size and proportion of variance for a twoindependent sample ttest 0 Estimated Cohen s dcan be used to estimate the effect size for the two independent sample ttest This measure estimates how far or how many standard deviations an observed mean difference shifted in one or two populations The formula for estimated Cohen s dfor the twoindependent sample t testis 0 M1 M2 square root of squot2p o The computation and interpretation of proportion of variance are the same for all ttests o Summarize the results of a onesample ttest and a twoindependent sample ttest in APA format 0 To report the results of a onesample ttest and a twoindependent sample t test state the Test statistic degrees of freedom p value and effect size 0 In addition a gure or table is often used to summarize the means and standard error or standard deviations measured in a study While this information can be included in the written report it is often more concise to include it in a table or gure Chapter 1 0 0 Describe two types of research designs used when we select related samples 0 In a related sample participants are related Participants can be related in one of two ways 0 They are observed in more than one group 0 RepeatedMeasures Design 0 They are matched either experimentally or naturally based on common characteristics or traits o MatchedPairs Desidn oThe repeatedmeasures design is a research design in which the same participants are observed in each treatment Two types of repeated measures designs are the prepost design and the withinsubjects design oThe matchedpairs design is a research design in which participants are selected then matched either experimentally or naturally based on common traits oExplain why difference scores are computed for the relatedsamples ttest oTo test the null hypothesis we state the mean difference between paired scores in the population and compare this to the difference between paired scores in a sample oA relatedsamples ttest is difference from a twoindependent sample ttest in that we rst nd the difference between the paired scores and then compute the test statistic oThe difference between two scores in a pair is called a difference score o Computing difference scores eliminates betweenpersons error This error is associated with differences associated with observing difference participants in each group or treatment Because we observe the same or matched participants in each treatment not different participants we can eliminate this source of error before computing the test statistic Removing this error reduces the value of the estimate of standard error which increases the power to detect an effect oCalculate the degrees of freedom for a relatedsamples ttest and locate critical values in the ttable also identify the assumptions for the related samples ttest and compute a relatedsamples ttest and interpret these results oThe relatedsamples ttest is a statistical procedure used to test hypotheses concerning two related sampled selected from related populations in which the variance in one or both populations is unknown oThe degrees of freedom for a relatedsamples ttest is the number of difference scores minus 1 oTo compute a relatedsamples ttest we assume normality and independence within groups The test statistic for a relatedsamples ttest concerning the difference between two related samples is M as s tobt P QWheresMD D 0 Compute effect size and proportion of variance for a relatedsamples ttest 0 Estimated Cohen s dis the most popular estimate of effect size used with the t test It is a measure of effect size in terms of the number of standard deviations that mean difference scores shifted above or below the population mean difference stated in the null hypothesis To compute estimated Cohen s dwith two related samples divide the mean difference Md between two samples by the standard deviated of the difference scores Sd 0 Another measure of effect size is proportion of variance I Speci cally this test is an estimate of the proportion of variance in the dependent variable that can be explained by a treatment Two measures of proportion of variance for the relatedsamples ttest are etasquared and omegasquared These measures are computed in the same way for all ttests 0 State three advantages for selected related samples 0 They can be more practical 0 They reduce standard error 0 They increase power

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