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Paired Samples t tests.docx

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Ohio State University
PSYCH 2220

T tests  Single Sample t-Test - compares sample mean to a specified value (population)  Independent Samples t-test - compares means of two independent samples  Paired samples t-test - comparing means of two dependent samples Each case consists of a pair of data points - one data point from each of the two samples Data points can be paired by:  Repeated-measures design - participants provide data at two points in time o Longitudinal research - follows participants over time o Pre-post design - participants measured on dependent variable before and after an intervention  Within subjects design- same participants measured in two different situations or under two different conditions o Ex: measure study retention in silence and with music with same participants  Matched pairs - participants are grouped by the researcher into sets of two based on their being similar on potential confounding variables o Dean comparing GPAs of male and female students may match students based on IQ into male/female pairs - can't argue that intelligence was a confounding variable if one sex has higher GPA Characteristics of Paired Samples Tests  Each condition in a dependent samples study is considered a "sample"  Adv. Over independent samples design - controls for individual differences - attributes that vary from case to case  Same participants are in both groups, research can be sure two samples are comparable in terms of background characteristics, more confident observed differences between groups on dependent variable is due to independent variable and not confounding variable  Multiple names for the same test - paired samples t test, dependent samples t test, correlated samples t test, related samples t test, matched pairs t test, within subjects t test, repeated measures t test  Often used o Pre-post design - where dependent variable is measured before and after the independent variable is applied o Controlling individual differences makes studies that use paired samples more powerful than studies that use independent samples - means probability of being able to reject null is higher - need a smaller sample size for paired samples than independent samples Example: compare wound healing time. Matched pairs of women with same socioeconomic status and age, but one person is a caregiver for someone with alzheimers. B/c they are matched on possible confounding variables (age, socioeconomic status) can't say that those would be cause of differences. Looking at stress of caring for another person as independent variable on dependent variable of wound healing time. 9.2 Calculating the Paired Samples t Test Study example: Six volunteers tested in temperature and humidity controlled chamber twice over a period of two days. Chamber set at 76 degrees, once with low humidity, once with high humidity (condition counter-balanced). Participant's perceived temperature is the dependent variable measured. Difference between perceived low-humidity and perceived high-humidity temperatures calculated, means, and standard deviations. Step 1. Pick a Test  Within-subjects design  Sample of people measured in two different conditions  Two-dependent samples  Comparing means of dependent samples - paired samples t-test Step 2. Check the Assumptions Random sample: sample is random from population Robust to violation Independence of observations: each case within a group or condition Not robust to is independent of the other cases in that group or condition violation Normality - population of difference scores is normally distributed Robust to violation Random - no, convenience sample Observations are independent within a sample - refers to independence within a sample, not between samples - same case in both samples or conditions, two samples are NOT independent. But each person is tested individually and each person is only tested once in each condition - so Independence of observations I NOT violated. Normality - that in the larger population, difference scores are normally distributed - difference scores are needed to calculate paired-samples t-test. 6 is a small sample size for making decisions about parent population, based on previous research, she proceeds. Calculation for Difference Score (D) D = X1 - X2 D = difference score being calculated X1 = a case's score in condition 1 X2 = a case's score in condition 2 Does not matter which value is subtracted from the other, as long as same order is followed for all cases. Step 3: List the Hypotheses  Statements about populations  Same as they were for independent samples t-test  Null says population means are the same Alternative says two population means differ - won't indicate whether difference is large/small,  positive/negative  Non-directional, two tailed  Two possibilities: o Low-humidity is perceived as hotter than high humidity o High humidity is perceived as hotter than low humidity o Ho:ulowhumidityuhighhumidity o Ha:ulowhumidityuhighhumidity  If a prediction had been made before-hand that high humidity would lead to higher perceived temperature, then it would be o Ho:ulowhumidityuhighhumidity o Ha:u < u lowhumidity highhumidity Step 4: Set the Decision Rule  Formulated same as for independent samples t test  Critical value based on: o Number of tails o How willing you are to make a Type I error (alpha level) o How many degrees of freedom there are  Degrees of freedom o df = N-1 o N = the number of pairs of cases  Critical value marks rare zone - where null hypothesis is rejected and common zone - where it is not  When drawing on a chart - t=0 Step 5: Calculate the Test Statistic  Same general procedure as was used in independent samples t  Divide the difference between the two sample means by the standard error of the difference  Standard error of the difference is the standard error of the difference for difference scores abbreviated SMD  Standard error of the difference for difference scores is the standard deviation of the sampling distribution of difference scores Calculating the Standard Error of the Difference for Difference Scores (S ) MD SMD = SMD = standard error of the difference for difference scores SD= standard deviation(s) of the difference scores N = number of pairs of cases Calculate SDby doing the following equations using the dif
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