Ttest

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Lecture 14

• T-test

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When do we use t-test?

• To examine differences between two groups
  measured on an interval/ ratio dependents
  variable
• Independent variable categorical variable
• Dependent variable numerical variable

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Example

• Is there any difference between female and male
  students with regard to their performances in the
  final exam?

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Female Male
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I. Calculating t value

• Formula
• T

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Steps

• Calculate the mean for each group
• ex) Females mean 8
• Males mean 6
• 2. For the first group, subtract the mean from
  each of the scores to get the deviation scores.
  Do the same for the second group.
• 3. For the first group, square the deviation
  scores and then add them together to get the sum
  of squares. Do the same for the second group.

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• ex) Female
• (SS sum of the squares 6)

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• Ex) Male
• (SS 2)

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• 4. Subtract the mean of group 2 form the mean of
  group 1
• ex) 8 6 2
• 5. Add together the sum of squares for both
  groups and divide by the number of participants
  minus 2
• ex) 6 2 / 5 5 2 1
• 6. Divide the total number of participants by the
  number of participants in group 1 multiplied by
  the number of participants in group 2
• ex) 5 5 / 5 5 0.4

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• 7. Multiply the result of step 5 by the result of
  step 6
• ex) 1 0.4 0.4
• 8. Take the square root of 7
• ex) square root of 0.4 0.6
• 9. Divide the result of step 4 by step 8
• ex) 2 / 0.6 3.3 -gt t value

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II. Determine whether t value is significant

• Probability level (predetermined by the
  researcher) p lt .05
• Degrees of freedom (df)
• number of participants - 2

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Steps

• 1. Calculate the degrees of freedom, which equals
  the total number of participants minus 2 for
  independent samples
• ex) 10 2 8
• 2. Look up the critical value at the .05
  significant level with the appropriate degrees of
  freedom on the t table
• ex) critical value 2.306

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• 3. If the calculated value meets or exceeds the
  critical value, there is a difference between two
  groups. If the calculated value does not meet the
  critical value, there is no difference between
  two groups.
• ex) 3.3 gt 2.306