Exploration 1.5 Eye Dominance 35-1

R 5 T R L T Th%W-Based Ap e roac - ion z-test) In #sa, you probably de- scribed the shape of proach (One-Proportio! ) In vt A he null distribution using words such as bell-shaped. “mmm:f;'-f:‘::’c' s Tmal. You have seen many null distributions in this chapter that have had |\‘ . 3SIc shape. You should have also noticed that the null distributions have all been centered at the hypothesized value of the long-run proportion used in the null hypotheses. You probably could have predicted that your null distribution was going to be somewhat bcll-».\'hA\_Pc‘].3“.‘1 centered at 0.50, You pmh(abl\' would have a harder time predicting your null distribution's variability (standard deviation), but this too can be predicted in advance, as we will see shortly. We can use mathematical models known as normal distributions (bell-shaped curves) 0 approximate many of the null distributions we have generated so far in this text. When rules and theories are used to predict what the value of the standardized statisti ic and p-value would be if someone carried out a simulation, we call the approach a theory-based approach. 'lrhC normal distribution provides a second way, in addition to simulation, to approximate a p-value. 6. Check the box next to Normal Approximation in the applet. Does thg rcgiog shadc.d in blue seem to be a good description (model) of what we actually got in the simulation? \l < Aw \ | { o 45 A\ it 1 qall§ Validity Conditions for Theory-Based Approach The normal approximation to the null distribution is valid whenever the sample size is reasonably large. One convcn.uon i to consider the sample size to be large enough whenever there are at least 10 observations in each category. 7. According to this convention, is the sample size large enough in this study to use the normal approximation and theory-based inference? Justify your answer. \ M gd R s Yie Sl ey S \ Validity Conditions The normal approximation can be thought of as a prediction of what would occur if a simulation-based analysis was carried out. Many times this prediction is valid, but not always. It is only valid when the condition (at least 10 successes and at least 10 failures) is met. Formulas The normal approximation will also give you values of the standardized sta- tistic and p-value based on its mathematical predictions. As you learned in Section 1.3, the standardized score is calculated as _statistic — mean of null distribution ~ “standard deviation of null distribution The mean of the null distribution is the hypothesized value of the long-run propor- tion (7). The standard deviation can be obtained in two ways: First, find the standard deviation of the null distribution by simulating. Second, predict the value of the standard deviation by substituting into this formula: VaQl -m)/n. Exploration L5 Eye pominance 35