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# Psych 2220 review of ch. 9, and what to know for 10 and 11 Psych 2220

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one sample t tests practice z statistics for a sample t statistics for one sample t statistics for paired sample one sample vs. paired sample t t statistics for paired samples t statistics f...
COURSE
Data Analysis in Psychology
PROF.
Joseph Roberts
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
psych 2220, Data Analysis, t tests, practice, z statistics, one sample, paired sample, t statistics, Statistics, z statistic, t statistic, independent samples, confidence intervals, Psychology, neuroscience, OSU, ohio state, effect sized, cohens d, d hat
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This 4 page Class Notes was uploaded by MadsSwart on Sunday March 6, 2016. The Class Notes belongs to Psych 2220 at Ohio State University taught by Joseph Roberts in Winter 2016. Since its upload, it has received 16 views.

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Date Created: 03/06/16
One Sample t-tests Practice Problems [worked out] 1. Mean = 2.81 SD=1.61 N=16 a. What z score would correspond to an observed value of 5? z=x−μ z= 5−2.81=1.36 b. σ  1.61 c. This was just a sample drawn from a population with µ=3 and σ=1.5 i. Mean; M=2.81 SD; s=1.61 N=16 ii. How likely is it to draw a sample N=16 whos mean is as extreme as 2.81? M−μ M M−μ M M=¿ = 2.81−3 σ M σ 1.5 1. √N = = -.51; Z √16 ¿ p=.61 iii. Calculate a one-sample t statistic for this sample, compared to a hypothesized population mean of 3. What do we conclude? 2.81−3 t( ) = 1.61 iv. = -.47; p=.65 √16 1. Table B-2: Critical Values in t distributions t(15) = -.4715 is the df (df=N-1) 2. Decision about the Null 1. We fail to reject H that µ=3 0 v. What values could we confidently identify as possible population means for the average approval level? Mupper samplcritM) 1. 95% confidence level M =M −t ∗ s lower samplcritM) 1. 2.81 = (2.132 x (1.61/√16)) =3.66 2. 2.81 – (2.132 x (1.61/√16)) =1.96 i. {1.96,3.66} 2. Mean 1: M=2.25 SD: s=1.44 N =16 Mean 2: M=281 SD: s=1.61 N 116 Difference: M=.56 SD: s=1.03 N D16 Taking these difference scores as a set of values, can we formulate and test hypotheses about the change in approval over time H 1 mean difference does not equal zero H 0 mean difference equals zero; zero difference 0.56−0 difference=¿ 1.03 √16 =2.18 t¿ - One sample t statistic computed for difference scores is fully equivalent to a paired-samples t statistic computed on the original pre- and post- scores. REVIEW OF CONCEPTS 1. Z statistics for a sample a. Z statistic can also refer to the mean x value for a sample of size N b. It represents a single observed mean in terms of its distance from the center of the sampling distribution of the mean – in terms of the population standard deviation σ i. Use σ to compute σ M 2. t statistics for one sample a. Converted version of a regular observed value for a sample mean b. Represents a single observed mean in terms of its distance from the center of the sampling distribution of the mean, as estimated by the observed sample standard deviation s. i. We use s to compute s w 3. t statistics for paired samples a. converted version of a regular observed z statistic for a sample mean b. it can also represent a single observed mean difference between two related observations, in terms of that difference’s distance from the center of the sampling distribution of the mean difference, as estimated by the observed sample difference standard deviation s D i. we use s to compute s D mean_difference 4. one sample t vs. paired samples t a. one sample t i. it represents a single observed mean in terms of its distance from the center of the sampling distribution of the mean, as estimated by the observed sample standard deviation, s. b. paired sample t i. represents a single observed mean difference between two related observations, in terms of its distance from the center of the sampling distribution of sample standard deviation of differencesDs 5. t statistics for paired samples a. This is all pretty much what we need to know for chapter 10 b. when and how to compute the difference between related observations c. set that group of difference scores as your one sample of scores for a one-sample t test d. exception: effect size estimates for paired samples are not always so directly analogous to the one-sample approach 6. t statistics for independent samples a. unrelated samples or non-paired samples b. one sample t test compares an observed sample mean to a population mean c. independent samples t test compares an observed sample mean to another observed sample mean (M and M ) A B i. there are complexities in estimating variability for this situation d. if the samples are actually independent, then the scores vary independently of each other i. need to add the two samples’ variances together within the t-statistic formula we’ve been using ii. exactly how we do that is just a matter of implementation 1. and there’s chapter 11 7. confidence intervals for t tests a. σM  s M critical z  critical t b. Confidence intervals for the mean i. When hypothesis-testing, we’re asking whether a sample mean deviates from a true population mean. Implicitly, we’re trying to estimate the true population mean 1. Our sample mean M is a point estimate of µ 2. We can build an interval around M that describes a range of values that we are confident will include µ a.Use t criticald solve for µ upperand µ lower b.Z criticaltcritical 8. Effect sizes a. Should we care about this observed difference from the population mean? i. It is important in the sense of a big effect? ii. Big effects might still not be significant. Recall similar distinction between strong vs. significant correlations b. Extent of difference between means (observed mean and population mean) i. Alt: the extent to which participants’ mean exceeded the value expected by chance (H 0 c. Estimated effect size i. Already calculated effect size scaled directly to sigma ii. Now scale to our estimate of sigma – estimated by s iii. We call the first equation, d-hat 1. But just refer to it as cohen’s d (M−μ) d= σ (M−μ) d= σ

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