17.1.3

t-Tests

Test yourself

Hypothesis Testing

A hypothesis is an assumption made about the value of a particular parameter. We can use a tt-test to determine whether the difference between the means of two populations are statistically significant.

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Null and alternative hypotheses

  • The null hypothesis, H0H_0, is a hypothesis that is assumed to be correct. In a tt-test, the null hypothesis is that there is no significant difference between the two population means.
  • The alternative hypothesis, H1H_1 is that there is a significant difference between the two population means.
  • A decision is then made as to whether or not there is sufficient evidence to reject the null hypothesis.
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pp-value

  • In order to test a hypothesis, we consider how likely the hypothesis is to be true.
  • The probability of the null hypothesis being true is referred to as the pp-value.
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Significance level

  • If the probability of the null hypothesis being true is less likely than a given "significance level", we reject the null hypothesis.
  • The significance level used in biology is often 5%.
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Test statistic

  • The test statistic used to calculate pp-values is equal to:
    • t=x1x2s12n1+s22n2t = \frac{\large\overline{x}_1-\overline{x}_2}{\large \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}
    • x1\overline{x}_1 = is the mean of sample one.
    • x2\overline{x}_2 = is the mean of sample two.
    • s1s_1 is the standard deviation of sample one.
    • s2s_2 is the standard deviation of sample two.
    • n1n_1 is the number of measures in sample one.
    • n1n_1 is the number of measures in sample two.
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Degrees of freedom

  • The degrees of freedom is equal to n1+n22n_1+n_2-2.
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Determine the critical value

  • Once you have determined the value of the test statistic, you need to use a statistics table to determine the critical value.
  • The critical value will be the value at the significance level (5%) of your particular degrees of freedom.
    • If the calculated value is greater than the critical value, you reject the null hypothesis.
    • If the calculated value is less than the critical value, you accept the null hypothesis.

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