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Hypothesis Testing  Chi Squared Test
we fail to reject the null hypothesis. There is insufficient evidence at the 0.05 level to conclude that the data don't fit a Poisson probability model.
You should decide whether to use the onetailed or twotailed probability before you collect your data, of course. A onetailed probability is more powerful, in the sense of having a lower chance of false negatives, but you should only use a onetailed probability if you really, truly have a firm prediction about which direction of deviation you would consider interesting. In the chicken example, you might be tempted to use a onetailed probability, because you're only looking for treatments that decrease the proportion of worthless male chickens. But if you accidentally found a treatment that produced 87% male chickens, would you really publish the result as "The treatment did not cause a significant decrease in the proportion of male chickens"? I hope not. You'd realize that this unexpected result, even though it wasn't what you and your farmer friends wanted, would be very interesting to other people; by leading to discoveries about the fundamental biology of sexdetermination in chickens, in might even help you produce more female chickens someday. Any time a deviation in either direction would be interesting, you should use the twotailed probability. In addition, people are skeptical of onetailed probabilities, especially if a onetailed probability is significant and a twotailed probability would not be significant (as in our chocolateeating chicken example). Unless you provide a very convincing explanation, people may think you decided to use the onetailed probability after you saw that the twotailed probability wasn't quite significant, which would be cheating. It may be easier to always use twotailed probabilities. For this handbook, I will always use twotailed probabilities, unless I make it very clear that only one direction of deviation from the null hypothesis would be interesting.
Support or Reject Null Hypothesis
The probability that was calculated above, 0.030, is the probability of getting 17 or fewer males out of 48. It would be significant, using the conventional PP=0.03 value found by adding the probabilities of getting 17 or fewer males. This is called a onetailed probability, because you are adding the probabilities in only one tail of the distribution shown in the figure. However, if your null hypothesis is "The proportion of males is 0.5", then your alternative hypothesis is "The proportion of males is different from 0.5." In that case, you should add the probability of getting 17 or fewer females to the probability of getting 17 or fewer males. This is called a twotailed probability. If you do that with the chicken result, you get P=0.06, which is not quite significant.
You must choose your significance level before you collect the data, of course. If you choose to use a different significance level than the conventional 0.05, people will be skeptical; you must be able to justify your choice. Throughout this handbook, I will always use P If you are doing an experiment where the cost of a false positive is a lot greater or smaller than the cost of a false negative, or an experiment where you think it is unlikely that the alternative hypothesis will be true, you should consider using a different significance level.
Why does one 'accept' the null hypothesis on a …
In the olden days, when people looked up P values in printed tables, they would report the results of a statistical test as "PPP>0.10", etc. Nowadays, almost all computer statistics programs give the exact P value resulting from a statistical test, such as P=0.029, and that's what you should report in your publications. You will conclude that the results are either significant or they're not significant; they either reject the null hypothesis (if P is below your predetermined significance level) or don't reject the null hypothesis (if P is above your significance level). But other people will want to know if your results are "strongly" significant (P much less than 0.05), which will give them more confidence in your results than if they were "barely" significant (P=0.043, for example). In addition, other researchers will need the exact P value if they want to combine your results with others into a .
If the null hypothesis were true (i.e., no change from the prior year) we would have expected more students to fall in the "No Regular Exercise" category and fewer in the "Regular Exercise" categories. In the sample, 255/470 = 54% reported no regular exercise and 90/470=19% reported regular exercise. Thus, there is a shift toward more regular exercise following the implementation of the health promotion campaign. There is evidence of a statistical difference, is this a meaningful difference? Is there room for improvement?
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Hypothesis Testing  Chi Squared Test  Boston University
The significance level you choose should also depend on how likely you think it is that your alternative hypothesis will be true, a prediction that you make before you do the experiment. This is the foundation of Bayesian statistics, as explained below.
comparator distribution specified in the null hypothesis is a ..
The work on the previous page is all well and good if your probability model involves just two categories, which as we have seen, reduces to conducting a test for one proportion. What happens if our probability model involves three or more categories? It takes some theoretical work beyond the scope of this course to show it, but the chisquare statistic that we derived on the previous page can be extended to accommodate any number of k categories.
Chi Square Test  P Value  Statistical Hypothesis Testing
In the χ^{2} goodnessoffit test, we conclude that either the distribution specified in H_{0} is false (when we reject H_{0}) or that we do not have sufficient evidence to show that the distribution specified in H_{0} is false (when we fail to reject H_{0}). Here, we reject H_{0} and concluded that the distribution of responses to the exercise question following the implementation of the health promotion campaign was not the same as the distribution prior. The test itself does not provide details of how the distribution has shifted. A comparison of the observed and expected frequencies will provide some insight into the shift (when the null hypothesis is rejected). Does it appear that the health promotion campaign was effective?
as the basis for rejecting the hypothesis
In neither case would we be inclined to reject our hypothesis.
We can repeat the chisquare goodnessoffit test for the larger sample size (4,865 heads/8,135 tails).
Testing Your Null Hypothesis and Calculating ChiSquare 1
Suppose the Penn State student population is 60% female and 40% male. Then, if a sample of 100 students yields 53 females and 47 males, can we conclude that the sample is (random and) representative of the population? Use the chisquare goodnessoffit statistic to test the hypotheses:
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