Advanced Higher Geography

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Advanced Higher Geography

• Section 3 Student t-test

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Student T-test

• Student t-tests are used when we are testing the
  difference between 2 samples
• It can only be used when using interval or ratio
  data
• The Null hypothesis is always that the 2 means
  are the same
• The alternative hypothesis is always that they
  are different, or that one is greater than the
  other

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Formula
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Worked example

• A researcher wants to find out the difference
  between birth rates of more developed countries
  and less developed countries
• Write down the null hypothesis and the
  alternative hypothesis

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Worked example

• Null hypothesis There is no difference between
  the mean birth rates of more and less developed
  countries
• Alternative hypothesis There is a difference
  between the mean birth rates of more and less
  developed countries

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Step 1

• On your copy of the statistics table, calculate
  the mean of column 1 and 4.
• 14
• 40

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Step 2

• Calculate the standard deviation for group x and
  group y
• sx 2.36
• sy 8.73

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Step 3

• Calculate the standard error for group x and y
• SE of x 0.786
• SE of y 2.910

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Step 4

• Calculate t using the formula

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The value of t can be either positive or negative
so we can ignore the sign.
T -8.625
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Calculating degrees of freedom

• Calculate degrees of freedom using the number of
  data for each set.
• (nx-1)(ny-1)
• (9-1)(9-1)
• Degrees of freedom 16

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Critical values

• Look up the critical values for 16 degrees of
  freedom on the table
• The critical value from the table for 0.05 (95)
  is 2.12
• T -8.26
• Do we accept or reject the NH?

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Results

• As t(-8.625) is greater than the critical value
  (2.12) we can reject the NH and accept the AH
• If t is smaller than the critical value, we have
  to accept the NH (There is no evidence to
  support the AH)

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One and two-tailed tests
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One-tailed tests

• When the hypothesis you wish to test is framed so
  that the direction is clear
• E.g. AH Men are taller than women
• Separate table are used for critical values
• We will only be using two-tailed tests

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Two-tailed tests

• For when you are interested in whether a
  difference exists in any direction
• E.g. AH Men are a different height from women
• The null hypothesis is the same for both tests

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Your turn

• Complete tasks on worksheet A5 using the student
  t-test
• Answers
• Degrees of freedom 22
• T -8.572