Occupational Biomechanics

Independent t-testsUses a sampling distribution of differences between means1

The test statistic for independent samples t-testsRecall the general form of the test statistic for t-tests:

Recall the test statistic for the single sample t-test

Horizontal axis value = sample meanDistribution mean = mean of distribution of sample meansDistribution SD = SD of distribution of sample means123

So how about the independent samples t-test?

The test statistic for independent samples t-tests

Horizontal axis value = ?1

So how about the independent samples t-test?

The test statistic for independent samples t-tests

Horizontal axis value = difference between 2 sample means1

So how about the independent samples t-test?

The test statistic for independent samples t-tests

Distribution mean = ? 1

2

So how about the independent samples t-test?

The test statistic for independent samples t-tests

SD of sampling distribution = ? 11

the SD of the distribution of differences between 2 sample meansSo how about the independent samples t-test?

The test statistic for independent samples t-tests

SD of sampling distribution = ? 1

On the SD of the distribution:Look at the SD (SEM) in more detail

Where:1

What affects significance?Mean differenceWith larger observed difference between two sample means, it is less likely that the observed difference in sample means is attributable to random sampling errorSample sizeWith larger samples, it is less likely that the observed difference in sample means is attributable to random sampling errorSample SD:With reduced variability among the cases in each sample, it is less likely that the observed difference in sample means is attributable to random sampling errorSee applet:http://physics.ubishops.ca/phy101/lectures/Beaver/twoSampleTTest.html1

d of f for the test statisticThe d of f changes from the one-sample casecomparing two independent means

becomesIf the 2 groups are of equal size1

Reporting t-test in textDescriptive statistics for the time to exhaustion for the two diet groups are presented in Table 1 and graphically in Figure 1. A t-test for independent samples indicated that the 44.2 ( 2.9) minute time to exhaustion for the CHO group was significantly longer than the 38.9 ( 3.5) minutes for the regular diet group (t18 = - 3.68, p 0.05). This represents a 1.1% increase in time to exhaustion with the CHO supplementation diet. Should also consider whether the difference is meaningful see effect sizes, later1

Reporting t-test in tableDescriptives of time to exhaustion (in minutes) for the 2 diets.

Note: * indicates significant difference, p 0.05GroupnMean SDReg Diet1038.9*3.54CHO sup1044.22.861

Reporting t-test graphicallyFigure 1. Mean time to exhaustion with different diets.1

Reporting t-test graphicallyFigure 1. Mean time to exhaustion with different diets.1

Summary/Assumptions of theindependent t-testUse when the assumption of no correlation between the samples is validDont test for itjust examine whether the assumption is fairUse when the two samples have similar variation (SD)Test for in output (see next few slides)12

t-tests in SPSSFirst note the data format: one continuous variable (in this case, age)

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t-tests in SPSSSecond, run the procedure:

drag the test variable overand specify 1

t-tests in SPSSThird, check the output:N, Mean, SD, SEMsignificance (if = .05, then < .05 is significant)df = n-1 = 1912

independent-tests in SPSSFirst, check the data:One grouping variableOne test variable1

independent-tests in SPSSSecond, run the procedure:

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independent-tests in SPSSSecond, run the procedure:

1. slide variables over2. click define groups3. define groups12

independent-tests in SPSSThird, examine the output:N, Mean, SD, SEMtest for equal variances (> .05 is good)significance (if = .05, then < .05 is significant)1234