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Lecture 8

# Lecture 8, Mar 5.docx

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Brock University

Child and Youth Studies

CHYS 3P15

Patricia Kirkpatrick

Winter

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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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