Although we now have strong evidence that professional graphologists really are

Question

Although we now have strong evidence that professional graphologists really are doing better than chance, there is an obvious question to be asked. Are they doing any better than you or I could do? Does the interpretation of handwriting require knowledge of the advanced graphological principles that the graphologists used to claim or is it just common sense? The BBC study also investigated this. They gave the handwriting samples to lay-people (people like you and me) as well as graphologists. The lay-people got 62% correct, compared with the graphologists, 66.7% correct. In truth, the 62% is an estimate and is subject to statistical error. Just like the 66.7% is. However, we will ignore this fact for the purposes of this assignment, and pretend that we know exactly that the probability of getting a correct answer for a lay-person is 0.62. Let's test whether we have evidence that the graphologists were doing better than lay-people from their 400/600 correct answers. (g) Select an appropriate method that you can use to decide whether or not the scores of the graphologists in the full study indicated a performance better than the lay-person's probability of 0.62, and apply the method to reach your conclusion, showing all appropriate formulation and working. (h) You should have found in part (g) that the improvement of graphologists over laypeople was statistically significant. Does this mean that the result has practical significance? Explain the difference between statistical significance and practical significance. Your answer should include a reference to the role of sample size in statistical significance.

Explanation / Answer

here we use the test of proprotion and we use z-test with

null hypothesis H0:P=0.62 and

alternate hypothesis H1:P>0.62

z=(p-P)/SE(p)=(0.667-0.62)/0.0198=2.37

SE(p)=sqrt(p(1-p)/n)=sqrt(0.62*(1-0.62)/600)=0.0198

here level of signigicance (alpha) is not mentioned ,let alpha=0.05

the one-tailed critical z(0.05)=1.645 is less the calculated z=2.37, so we reject null hypothesis and conclude that improvement of graphologists over laypeople was statistically significant.

(h)Practical significance asks the larger question about differences wether the differences between samples big enough to have real meaning.

Significant differences (i.e., reject the null hypothesis) means that differences in group means are not likely due to sampling error. The problem is that statistically significant differences can be found even with very small differences if the sample size is large enough. •In fact, differences between any sample means will be significant if the sample is large enough.

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