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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 σ x = 2.36 σ y = 8.73

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Step 3 Calculate the standard error for group x and y SE of x= SE of y= 2.910

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Step 4 Calculate t using the formula

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T= The value of t can be either positive or negative so we can ignore the sign.

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Calculating degrees of freedom Calculate degrees of freedom using the number of data for each set. [(n x -1)+(n y -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= 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 A 5 using the student t-test Answers: Degrees of freedom – 22 T =

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