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Lecture Quantitative investment analysis: Chapter 7 – CFA Institute

Chapter 7 – Hypothesis testing. This chapter include objectives: Define a hypothesis and describe the steps of hypothesis testing, define a hypothesis and describe the steps of hypothesis testing, distinguish between one-tailed and two-tailed tests of hypotheses,. | Hypothesis testing 1 Hypothesis testing The process of making judgments about a large group (population) on the basis of a small subset of that group (sample) is known as statistical inference. Hypothesis testing, one of two fields in statistical inference, allows us to objectively assess the probability that statements about a population are true. Because these statements are probabilistic in nature, we can never be certain of their truth. Steps in hypothesis testing Stating the hypotheses. Identifying the appropriate test statistic and its probability distribution. Specifying the significance level. Stating the decision rule. Collecting the data and calculating the test statistic. Making the statistical decision. Making the economic or investment decision. 2 H0= ? Ha= ? LOS: Define a hypothesis and describe the steps of hypothesis testing. Pages 243–244 It is worth spending time on Steps 1 and 2 at this stage. The statements of the null and alternative hypotheses are often where . | Hypothesis testing 1 Hypothesis testing The process of making judgments about a large group (population) on the basis of a small subset of that group (sample) is known as statistical inference. Hypothesis testing, one of two fields in statistical inference, allows us to objectively assess the probability that statements about a population are true. Because these statements are probabilistic in nature, we can never be certain of their truth. Steps in hypothesis testing Stating the hypotheses. Identifying the appropriate test statistic and its probability distribution. Specifying the significance level. Stating the decision rule. Collecting the data and calculating the test statistic. Making the statistical decision. Making the economic or investment decision. 2 H0= ? Ha= ? LOS: Define a hypothesis and describe the steps of hypothesis testing. Pages 243–244 It is worth spending time on Steps 1 and 2 at this stage. The statements of the null and alternative hypotheses are often where individuals will struggle. You will often encounter questions like “Is the null what I want to show or what I don’t want to show?” This creates an immediate tension because any truly scientific process should be devoid of “want” and be totally objective. Rather, think more along the lines of what can and can’t be demonstrated. 2 1. State the hypothesis The foundation of hypothesis testing lies in determining exactly what we are to test. We organize a hypothesis test into two categories. The null hypothesis, denoted H0, is the hypothesis we are testing. The alternative hypothesis is denoted Ha. The different possibilities represented by the two hypotheses should be mutually exclusive and collectively exhaustive. Three different ways of formulating a hypothesis test: H0: θ = θ0 versus Ha: θ ≠ θ0 (a “not equal to” alternative hypothesis) H0: θ ≤ θ0 versus Ha: θ > θ0 (a “greater than” alternative hypothesis) H0: θ ≥ θ0 versus Ha: θ < θ0 (a “less than” alternative hypothesis) Hypothesis tests