StatTutor Lesson - The Idea of Analysis of Variance

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The idea of analysis of variance
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      Question 1

      48

      Question 1.

      What does the "observed variation" in the numerator of the F test statistic measure?

      A.
      B.

      Incorrect. "Observed variation" measures the variation between the sample means.
      Correct. "Observed variation" measures the variation between the sample means.
      Incorrect. Try again.
      2

      Question 2

      142

      Question 2.

      How much variation is there between the sample means in Case 1?

      A.
      B.

      Incorrect. There is no variation between the sample means in Case 1.
      Correct. There is no variation between the sample means in Case 1.
      Incorrect. Try again.
      2

      Question 3

      168

      Question 3.

      Fill in the blank: The "observed variation" between the sample means is ___________ the "expected variation" in the sample means if the population means are equal.

      A.
      B.
      C.

      Incorrect. The "observed variation" should be approximately equal to the "expected variation" if the null hypothesis is correct.
      Correct. The "observed variation" should be approximately equal to the "expected variation" if the null hypothesis is correct.
      Incorrect. Try again.
      2

      Question 4

      261

      Question 4.

      How much variation is there between the sample means in Case 2?

      A.
      B.

      Incorrect. There is a lot of variation between the sample means in Case 2.
      Correct. There is a lot of variation between the sample means in Case 2.
      Incorrect. Try again.
      2

      Questions 5-6

      275

      Question 5.

      Fill in the blank: The "observed variation" between the sample means is ___________ the "expected variation" in the sample means if the population means are NOT all equal.

      A.
      B.
      C.

      Incorrect. The "observed variation" will be much greater than the "expected variation" if the population means are not all equal.
      Correct. The "observed variation" will be much greater than the "expected variation" if the population means are not all equal.
      Incorrect. Try again.
      2

      Question 7

      420

      Question 7.

      Fill in the blank: For case 1 where the population means are equal, the "observed variation" between the sample means is _____________ the "expected variation" as measured by the variability of individuals within the samples.

      A.
      B.
      C.

      Incorrect. Since the population means are equal, the variation between the sample means is approximately equal to the variation within the samples.
      Correct. Since the population means are equal, the variation between the sample means is approximately equal to the variation within the samples.
      Incorrect. Try again.
      2

      Questions 8-9

      512

      Question 8.

      Fill in the blank: For case 2 where the population means are all different, the "observed variation" between the sample means is _____________ the "expected variation" as measured by the variability of individuals within the samples.

      A.
      B.
      C.

      Incorrect. Since the population means are all different, the variation between the sample means is much much greater than the variation within the samples.
      Correct. Since the population means are all different, the variation between the sample means is much much greater than the variation within the samples.
      Incorrect. Try again.
      2

      Question 10

      614

      Question 10.

      True or false: If the value of the F test statistic is approximately 1.0, then we will get a very small P-value and we will reject H0.

      A.
      B.

      Incorrect. If the value of the F test statistic is approximately 1.0, then we do not have evidence to reject H0 and the P-value will not be very close to zero.
      Correct. If the value of the F test statistic is approximately 1.0, then we do not have evidence to reject H0 and the P-value will not be very close to zero.
      Incorrect. Try again.
      2

      Question 11

      652

      Question 11.

      How should you compute the F test statistic and P-value for a one-way analysis of variance procedure?

      A.
      B.

      Incorrect. The computations are complicated and use of software is recommended.
      Correct. The computations are complicated and use of software is recommended.
      Incorrect. Try again.
      2