Advanced Higher STATISTICS Student’s t-test (testing the difference between 2 samples) t = Ẋ- ӯ √(SE of x) 2 + (SE of y) 2 A student’s t-test is a test.

Presentation on theme: "Advanced Higher STATISTICS Student’s t-test (testing the difference between 2 samples) t = Ẋ- ӯ √(SE of x) 2 + (SE of y) 2 A student’s t-test is a test."— Presentation transcript:

1 Advanced Higher STATISTICS Student’s t-test (testing the difference between 2 samples) t = Ẋ- ӯ √(SE of x) 2 + (SE of y) 2 A student’s t-test is a test of the difference between two samples. It is applied only to data measured on an interval or ratio scale. -The null hypothesis is always that the two samples are the same. -The alternative hypothesis states that the two means are different.

2 Advanced Higher STATISTICS Is there a difference between the two sets of data? SwitzerlandGermanyNorwayFrance Japan New Zealand USA SpainItaly ColombiaZambiaEgyptKenya India Brazil Bangladesh EthiopiaMali BIRTH RATE IN LEDCsBIRTH RATE IN MEDCs Use the students t-test to see if there is a significant difference, or not.

3 Null Hypothesis: there is no significant difference between the mean birth rates of more developed and less developed countries. Alternative Hypothesis: there is a significant difference between the mean birth rates of more developed and less developed countries. -2 -4 4 16 1 4 0 1 4 4 Switzerland - 12 Germany - 10 Norway - 13 France - 14 Japan - 16 New Zealand - 18 USA - 15 Spain - 16 Italy - 12 126 9 14 50 5.56 2.36 -10 11 -5 8 -7 -11 10 9 100 121 25 64 49 121 100 81 Colombia - 30 Zambia - 51 Egypt - 35 Kenya - 48 India - 35 Brazil - 29 Bangladesh - 33 Ethiopia - 50 Mali - 49 126 9 14 686 76.2 8.73 2 0 1 4 2 -2 2.36 √9 √ 8.73 √9 √ 0.7862.910 Use the students t-test to see if there is a significant difference, or not

4 Null Hypothesis: there is no significant correlation between percentage of soil moisture and altitude. Alternative Hypothesis: there is a significant correlation between percentage of soil moisture and altitude. t = Ẋ- ӯ √(SE of x) 2 + (SE of y) 2 t = 14 - 40 √0.617 + 8.469 t = -26 √9.086 t = -8.625 NOTE: The t-value can be positive or negative. For this test we can ignore the sign and just use the figure when we compare it against the critical value Now look to see if the calculated value of t is higher or lower than the critical value.

5 Null Hypothesis: there is no significant correlation between percentage of soil moisture and altitude. Alternative Hypothesis: there is a significant correlation between percentage of soil moisture and altitude. t = -8.625 Calculate degrees of freedom (n x – 1) + (n y – 1) (9-1) + (9-1) = 16 16 The calculated value of t is 8.62 which is higher than the critical value of 2.12 (95% confidence) and 2.92 (99%) so we can reject the null hypothesis and accept the alternative hypothesis that there is a significant difference between developing and developed countries birth rates.