Accuracy of Fingerprint Identifications An experiment was cond...

Question

Accuracy of Fingerprint Identifications An experiment was conducted to compare the accuracy of fingerprint experts to the accuracy of novices (based on data from “Identifying Fingerprint Expertise,” by Tangen, Thompson, and McCarthy, Psychological Science, Vol. 22, No. 8). The data in the table are based on trials in which the evaluators were given matching fingerprints. Use a 0.05 significance level to determine whether correct identification is independent of whether the evaluator is an expert or a novice.

Table comparing fingerprint identification accuracy: Novices 331 correct, 113 wrong; Experts 409 correct, 35 wrong.

Accepted Answer

Below there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A safety agency studied how experience affects drivers' ability to correctly identify traffic signs during a simulation. Two groups, licensed drivers and learner drivers, were shown standard road signs under timed conditions and were asked to identify them. The table below shows whether their responses were correct or incorrect. In our far right column, we have incorrect. In our middle column we have correct, and then our far left column for our two rows, we have licensed drivers and learner drivers. So licensed drivers who got correct answers was 68 and incorrect was 22. Learner drivers had 55 correct, and learner drivers had 45 incorrect. At a 0.05 significance level, test the claim that the correct identification is independent of the driver's experience level. Awesome. So it appears for this particular problem, we're asked to determine at the significance level of 0.05, we need to test the claim that the correct identification is independent of the driver's experience level. So now that we know what we're ultimately trying to solve for, first off, once again, for this particular prompt, as we should note and recall, we need to aim to test whether the accuracy of identifying traffic signs is independent of the driver's experience level, meaning if they're a licensed driver or a learner driver, for this particular prom, a T square test is appropriate. Because we are dealing with categorical data presented in a contingency table. And as we should recall a note, the G square test for independence is used to determine whether there is a significant association between two categorical variables. So, With that in mind, our first step is we need to state the hypothesis values. So for our null hypothesis, which will note this value as H0, so for our null hypothesis, as we should recall, for this particular case, the identification accuracy will be independent of the driver experience, and for our alternative hypothesis, which we'll call H1. The identification accuracy is not independent of driver experience. So now, our second step is we need to calculate the totals. So I've gone ahead. And created a table to help us calculate our totals. So as you could see, I took our table that was provided to us by the prom itself and I added a new far right column, which is the row total. Then our middle column is incorrect, and then our left column is correct, and then the far left column has 3 separate rows for licensed drivers, learner drivers, and column total. So for a column total for correct answers is 123, for incorrect, it is 67, and for row total, it's 190, and for licensed drivers, it's 90, and for learner's drivers, it's 100. Fantastic. So now, Our next step, our 3rd step now, is we need to Determine Our expected count. So we need to recall and use the following equation. So that means that for step 3, we need to recall and note that the margin of error E is equal to the row total multiplied by the column total. All divided by the grand total. Fantastic. So, with that said, We need to use this table to help us solve for this formula. So using the following table, we can use our formula to obtain the expected counts as follows, which from our table, which once again, I created another table. So for problems like this, sometimes it's helpful to like open an Excel spreadsheet and type data points in, so it does all the math for you. So, in our new table now that we're using, We have our, we have our values once again since we plugged in our values into our formula. So we found that our licensed driver correct is 58.26, and then licensed drivers incorrect is 31.74 for learner drivers, it's 64.74 for correct, and 35.26 for incorrect. Fantastic. So now, moving right along now, our fourth step is we need to compute the T2 test statistic, which, as we should recall, T2 is equal to the sum. Of, so when you take the sum of parentheses minus E to the power of 2 divided by E. And I said E is the margin of error, but to be specific, E in this particular case is the expected counts. You might also see E as margin of error, but in this case it's not margin of error. I should be specific. It is once again the expected counts. So, moving right along here, so using our new formula, we can create another table, and for our final table that we have to create for this particular problem to help us solve for our final answer, we have our, we I'll go by row. So our first row is we have cell, then we have our value for O, our value for E, and then we have our value for parentheses O minus E square divided by E. And for our cell column going down, we have license correct, licensed incorrect, learner correct, learner incorrect, and then the total key value. So going in order. For license correct, so it's 6858.26 and 1.628 and then for licensed incorrect, it's 22, 31.74 2.988 and then learner correct 55, 64.74 and 1.466. And then finally. Learner correct or incorrect. So learner incorrect is 45 35.26, and 2.691, and then our total key value is 8.773. Fantastic. So, that will mean moving right along here. That our step 5 is we need to determine our critical value. So we need to note and recall that our for our degrees of freedom, which I'll call DF for short, so our degrees of freedom will be equal to our row 1, which I'll just call our 1, rows 1. Multiplied by columns one, which I'll call C1. And this will be equal to, so DF will be equal to 2 minus 1 multiplied by 2 minus 1, which is going to be simply equal to 1. So that means we need to note and recall that our critical value, which we'll call alpha. Well, once again, we need to find our critical value, which once again, we need to note that our significance level alpha is equal to 0.05. So that would mean that our critical value will be at 3.841. Fantastic. So now, our sixth and final step is we need to make our final conclusions. So since the calculated G2 value is 8.773 is greater than the critical value of 3.841, we can reject the null hypothesis. So therefore, without a doubt, our final answer would be. There is sufficient evidence to conclude that the correct identification is not independent of driver experience, so that will mean that when we go back to the top to look. At our prom to summarize what we've learned, that will mean once again that our final answer without a doubt will have to be the following, and once again there is sufficient evidence to conclude that the correct identification is not independent of driver experience. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Chi-Square Test of Independence

Significance Level (α)

Contingency Table

Watch next