IBDP Mathematics Applications & Interpretations SL Chapter 8 Notes

Testing for validity: Spearman’s hypothesis testing and x^2 test for independence

STUDY NOTES FOR MATHEMATICS – CHAPTER 8– Testing for validity: Spearman’s hypothesis testing and x^2 test for independence

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In this chapter, we learn about the Spearman’s rank correlation coefficient of a bivariate data set, the Pearson product-moment correlation of coefficient of the variables’ ranks. We look at a more formal procedure to determine whether a statistical hypothesis is reasonable. This is known as a hypothesis test. The hypothesis tests include the Z test (used to test hypotheses about the mean of a normally distributed population with known variance), t-tests (when population variance is unknown) and hypothesis tests that consider other parameters such as population proportion or population correlation coefficient. These tests follow the same general procedure. First, we formulate statistical hypotheses. Then we choose the significant level for the test. Using data from a sample will help calculate a data statistic and then the p-value for the test statistic which can help us make decisions about the hypotheses. The final topic in this chapter takes a look at error probabilities and statistical power.

When we observe a variable in a population, we do not always know its distribution. If we choose a distribution to model the variable, we will want to know how well the distribution fits our observation. In this chapter, we study x2 (chi-squared) tests to assess how appropriate a statistical model is. In order to find the chi-squared goodness of the fit test, we first state the null hypothesis, state the significance level a, calculate the value of the test statistic, use technology to calculate the p-value, reject null hypothesis if p value < a, otherwise accept alternative hypothesis. Finally, interpret your decision in the context of the problem. The chapter also explains how when the parameters of the distribution of interest are unknown, we must estimate them from the data. Lastly this chapter deals with the critical regions and values and the chi-squared test for independence.