6. A researcher is comparing two multiple-choice tests with...

6. A researcher is comparing two multiple-choice tests with different conditions. In the first test, a typical multiple-choice test is administered. In the second test, alternative choices (i.e. incorrect answers) are randomly assigned to test takers. The results from the two tests are given below. Compare the two test results. | | Regular Test | Randomized Answer | | :--- | :--- | :--- | | Mean | 59.9 | 44.8 | | SD | 10.2 | 12.7 |

Transcript

00:01 Once again, welcome to a new problem.

00:05 This time we're dealing with descriptive statistics.

00:10 We're dealing with descriptive statistics.

00:12 And for the most part, when you're looking at the spread of data, or sometimes what we call the dispersion of data, you can use the standard deviation.

00:30 You can use the standard deviation, which is obviously going to be the square root of the variance.

00:40 And it depends what you're doing.

00:43 So we do have population standard deviation, and we also have sample standard deviation.

00:52 So sample standard deviation is the same as small.

01:02 So you're looking at small s, which is the square root of the variance.

01:07 And in terms of the bigger formula, we have sum of x minus x squared over the degrees of freedom.

01:16 We could also use the population standard deviation, which is a square root of the variance.

01:23 But this time, if we're dealing with numbers, we use the population mean and the sample.

01:31 So this is the population size, that's capital n, and this is the population mean.

01:44 So we do have population size and population mean.

01:47 We have the sample size also, and we also have the degrees of freedom, which is n minus 1.

02:00 So n minus 1 would be the degrees of freedom.

02:06 If we want to compare different samples, we have something called the coefficient of variation, the coefficient of variation symbolic cv.

02:25 The coefficient of variation is also known as the relative.

02:33 Standard deviation.

02:35 So it's known as the relative standard deviation.

02:39 And if you're looking at the relative standard deviation, what's going to happen is that you do have rsd relative standard deviation, which is the same as the coefficient of variation.

02:57 And to get the coefficient of variation, you take the standard, you take the standard, deviation, sometimes you call this sd and then you divide the standard deviation by the mean.

03:15 If it's a sample, you have x -bar and then you multiply that by 100%.

03:23 So you divide by the mean and then you multiply by the 100%.

03:34 So the coefficient of variation is a standardized measure.

03:46 So this is the same as a standardized measure of dispersion.

03:53 We're looking at standardized measure of dispersion.

03:57 That's the coefficient of variation.

04:01 And the dispersion we're looking at is the dispersion related to a probability.

04:07 Probability or frequency distributions.

04:16 We have both the probability and we also have the frequency distribution.

04:26 The hallmark of this is the lower the coefficient of variation, they'll less the variability of data...

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