Class Notes (811,155)
Brock University (11,942)
CHYS 3P15 (11)
Lecture 8

# Lecture 8, Mar 5.docx

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School
Brock University
Department
Child and Youth Studies
Course
CHYS 3P15
Professor
Patricia Kirkpatrick
Semester
Winter

Description
3P15, Mar 5, Lecture 8 Chapter 11 • t-Tests with the Two Samples • (Also, Paired Samples from Chapter 10) Paired SAMPLES Measuring Association between Dummy and Interval/Ratio Variables with the Same Group Measured Twice • One of the challenges of using longitudinal surveys is comparing the same sample at two points in time. • This procedure is known as paired samples t-tests, repeated measures t-tests, or t- tests for dependent samples. • To use the same sample at each point in time, we focus only on the difference between scores for the first and second times. Independent Samples When do we use a two-sample test? • When we have two independent samples, and we are interested in testing whether there is a difference between them (between the populations) • The t-test is used to compare the value of an interval/ratio variable across two values of another variable o E.g., difference in the income of males and females. One- and Two-Tailed Tests, Again • One-tailed tests measure the significance and direction of a relationship – e.g. predict a significant difference between wages of men and women, and that men make more • There is no statistical reason for choosing a one-tailed test over a two-tailed test—the choice is theoretically driven. • If you are trying to determine whether or not groups are equal, use a two-tailed test. – e.g. know that historically men made more than women, but let’s say a lot of factories that men are working at are closing… you may predict that these would be more similar, but aren’t sure One- and Two-Tailed Tests, Again (cont’d) • If you believe that a group has more, or less, of a quality than another group, use a one- tailed test. • To use a one-tailed test, a slight modification of the two-tailed case is needed. • The modification is the use of a different value from the z- or t-table (or, divide p value in half in SPSS) Two-tailed v. One-tailed test • Two tailed, think there will be a difference, but not sure which way the relationship will go, e.g. whether men or women will make more… because we aren’t sure have to have 2.5% chance of difference being negative and 2.5% chance of difference being positive • If you are very certain that the relationship will go one way, can do a one tailed test and put your full 5% chance of error on one side Differences between Means in Two Samples • Often we are interested in comparing two unrelated or distinct groups, but we only have sample information (we have no values for σ and µ). • The equations and symbols differ, but the basic logic as that used in a t-test prevails. Differences between Means in Two Samples: An Example • Middle class families average 8.7 (N =871 s =3.1) email messages and working class families average 5.7 (N =27, s =223) messages. • The middle class families seem to use email more but is the difference significant at a 95% confidence level? Differences between Means in Two Samples: An Example (cont’d) • Don’t worry about the math 2 2  N 1 1 N s 2 2 N 1 N 2  s X1−X2 =     N 1 N −2  N 1 2   87*3.4 +57*2.3 2 87+57  =     87+57−2 87*57  = 0.52 t = X 1 X 2 = 8.7−5.7 = 5.77 s 0.52 X1−X2 The t-test Level of Significance for One-tailed Test 0.1 0.05 0.025 0.01 0.005 0.001 Level of Significance for Two-tailed Test df 0.2 0.1 0.05 0.02 0.01 0.002 91 1.291 1.662 1.986 2.368 2.631 3.182 92 1.291 1.662 1.986 2.368 2.630 3.181 93 1.291 1.661 1.986 2.367 2.630 3.180 94 1.291 1.661 1.986 2.367 2.629 3.179 95 1.291 1.661 1.985 2.366 2.629 3.178 96 1.290 1.661 1.985 2.366 2.628 3.177 97 1.290 1.661 1.985 2.365 2.627 3.176 98 1.290 1.661 1.984 2.365 2.
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