Caution: An outcome can be statistically significant, and it may or may not be important. Don’t associate statistical significance with importance. The Microsort XSORT gender selection technique was designed to increase the likelihood that a baby will be a girl. At one point before clinical trials of the XSORT gender selection technique were discontinued, 945 births consisted of 879 baby girls and 66 baby boys (based on data from the Genetics & IVF Institute). The probability of getting such results by chance with no treatment is 0.00000000 when rounded to eight decimal places. We can now interpret that probability to conclude that 879 girls in 945 births is a significantly high number of girls. For now, let’s consider this simpler problem that can be easily solved using the methods of this chapter: If a test of the XSORT method of gender selection involves 20 couples who give birth to 20 babies, what is the probability that the 20 babies are all girls? Does the result of 20 girls suggest that the XSORT technique is effective? We will address these questions in this chapter. In addition to being great fun, the topic of probability is critically important because it serves as a foundation for later concepts of statistics, such as hypothesis testing introduced in Chapter 8. Probability is not an independent and unrelated topic stuck in here for the sole purpose of being a fun distraction. Instead, probability plays an important role in helping us to determine whether results are significant. The main objective of this chapter is to develop a sound understanding of probability values, and then use those values to identify when results are significant. Probability values constitute the underlying foundation on which methods of inferential statistics are built. The important methods of hypothesis testing commonly use P-values, which are probability values expressed as numbers between 0 and 1, inclusive. Smaller probability values, such as 0.01, correspond to events that are very unlikely. Larger probability values, such as 0.99, correspond to events that are very likely. Here are the chapter objectives: 4-1 Basic Concepts of Probability • Identify probabilities as values between 0 and 1, and interpret those values as expressions of likelihood of events. • Develop the ability to calculate probabilities of events. • Understand and apply the rare event rule for inferential statistics to determine when results are significant. • Define the complement of an event and calculate the probability of that complement. 4-2 Addition Rule and Multiplication Rule • Develop the ability to calculate the probability that in a single trial, some event A occurs or some event B occurs or they both occur. Apply the addition rule by correctly adjusting for events that are not disjoint (or are overlapping). • Develop the ability to calculate the probability of an event A occurring in a first trial and an event B occurring in a second trial. Apply the multiplication rule by adjusting for events that are not independent. • Distinguish between independent events and dependent events. Chapter Objectives 143 CHAPTER OBJECTIVES >>>
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