Ch. 9 - Inferences from Two Samples

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 9 - Inferences from Two Samples

Problem 9.4.4

Chapter 9, Problem 9.4.4

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Verified step by step guidance

Understand the term 'robust': In statistics, a test is considered robust if it remains valid and reliable even when its assumptions are violated to some extent. For the F-test, one key assumption is that the data in each group being compared comes from a normal distribution.

Identify the assumption of normality: The F-test assumes that the populations being compared are normally distributed. This means that the shape of the data distribution in each group should resemble a bell curve.

Explain the impact of non-robustness: When we say the F-test is 'not robust against departures from normality,' it means that if the data significantly deviates from a normal distribution (e.g., it is skewed or has heavy tails), the results of the F-test may no longer be accurate or reliable.

Discuss potential consequences: If the assumption of normality is violated, the F-test may produce incorrect p-values, leading to an increased risk of Type I errors (rejecting a true null hypothesis) or Type II errors (failing to reject a false null hypothesis).

Suggest alternatives: In cases where normality is violated, consider using non-parametric tests (e.g., the Kruskal-Wallis test) or transforming the data to better meet the normality assumption before applying the F-test.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

F Test

The F test is a statistical method used to compare variances between two or more groups. It helps determine if the group means are significantly different from each other, based on the ratio of variances. The test assumes that the data follows a normal distribution and is commonly used in ANOVA (Analysis of Variance) to assess the impact of one or more factors.

Normality Assumption

The normality assumption refers to the requirement that the data being analyzed should follow a normal distribution for certain statistical tests, including the F test. When this assumption is violated, the results of the test may become unreliable, leading to incorrect conclusions about the significance of the differences between groups.

Robustness in Statistics

Robustness in statistics refers to the ability of a statistical test to remain valid under violations of its assumptions. A test is considered robust if it can still provide reliable results even when the data deviates from the ideal conditions, such as normality. The F test is described as not robust against departures from normality, meaning that its results can be significantly affected when the data does not follow a normal distribution.

Recommended video:

Guided course

05:53

Parameters vs. Statistics

Related Practice

Textbook Question

Test for Normality For the hypothesis test described in Exercise 2, the sample sizes are n1 = 2208 and n2 = 1986 When using the F test with these data, is it correct to reason that there is no need to check for normality because both samples have sizes that are greater than 30?

159

views

Textbook Question

Randomization vs t Test Two samples of commute times from Boston and New York are randomly selected and it is found that the samples sizes are n1 = 18 and n2 = 12 and each of the two samples appears to be from a population with a distribution that is dramatically far from normal. Which method is more likely to yield better results for testing Mu1 is not equals to Mu2. Hypothesis test using the t distribution (as in Section 9-2) or the resampling method?

101

views

Textbook Question

No Variation in a Sample An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the two sample groups come from populations with the same mean.

142

views

Textbook Question

Is Friday the 13th Unlucky? Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad for Your Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we want to use a 0.05 significance level to test the claim that the data support the claim that fewer hospital admissions due to traffic accidents occur on Friday the 6th than on the following Friday the 13th. Identify the null hypothesis and alternative hypothesis.

132

views

Textbook Question

Degrees of Freedom In Exercise 20 “Blanking Out on Tests,” using the “smaller of n1-1 and n2-1” for the number of degrees of freedom results in df=15 Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by using Formula 9-1 instead of the “smaller of n1-1 and n2-1 ”?

133

views

Textbook Question

Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Use a 0.05 significance level to test the claim that creative task scores have the same variation with a red background and a blue background.

[Image]

137

views