A paired-samples t-test compares the means of two related sets of data to see if they differ statistically. IQ Example We may want to compare the IQ scores.

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Presentation transcript:

A paired-samples t-test compares the means of two related sets of data to see if they differ statistically. IQ Example We may want to compare the IQ scores of a group of students at the beginning and end of their degrees to see if there is any change. We take IQ measurements of 10 students at the beginning of their degrees, and IQ measurements from the same 10 students at the end of their degrees.

Does the mean IQ of the students change over the course of their degrees? Student Number Start IQ End IQ 1 111 110 2 116 117 3 114 4 109 5 115 6 124 122 7 106 8 9 113 10

STEP 1: Calculate the mean difference between pairs Start IQ End IQ D 111 110 1 116 117 -1 114 -3 109 115 4 124 122 2 106 113

STEP 1: Calculate the mean difference between pairs Is this mean difference significantly different from zero? (this is what a paired-samples t-test determines)

STEP 2: Calculate Standard Deviation of differences 1 -1 -2 4 -3 -4 16 3 9 2

STEP 2: Calculate Standard Deviation of differences

STEP 3: Compute the t-statistic

STEP 4: Compute the Degrees of Freedom

Significance Level (α) STEP 5: Look-up Critical t-value in Table of Values df Significance Level (α) 0.1 0.05 0.01 1 6.314 12.706 63.657 2 2.920 4.303 9.925 3 2.353 3.182 5.841 4 2.132 2.776 4.604 5 2.015 2.571 4.032 6 1.943 2.447 3.707 7 1.895 2.365 3.499 8 1.860 2.306 3.355 9 1.833 2.262 3.250 10 1.812 2.228 3.169 11 1.796 2.201 3.106 12 1.782 2.179 3.055

STEP 6: Compare t-statistic with Critical t-value Calculated t-statistic = 1.25 Critical t-value = 2.262 If calculated t-statistic is larger than critical t-value: SIGNIFICANT If calculated t-statistic is smaller than critical t-value: NON-SIGNIFICANT The calculated t-statistic is smaller than the critical t-value, therefore the mean IQ of students at the end of their degrees (113) was not significantly different from the mean IQ at the start of their degrees (114).

Summarise Findings The IQ of students at the end of their degrees (M = 113) was not significantly different from the IQ at the start of their degrees (M = 114), t(9) = 1.25, p > .05.