In Exercises 1–4, use the following listed measured amounts of...

Question

In Exercises 1–4, use the following listed measured amounts of chest compression (mm) from car crash tests (from Data Set 35 “Car Data” in Appendix B). Also shown are the SPSS results from analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different car sizes have the same mean amount of chest compression.

Anova

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

Table showing chest compression data (mm) for small, midsize, large cars, and SUVs from crash tests.

Anova

a. What characteristic of the data above indicates that we should use one-way analysis of variance?

Accepted Answer

Hello there. Today we're to 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 researcher collects data on the reaction times in units of milliseconds of drivers in response to 3 different types of traffic signals red, yellow, and green. The goal is to determine whether the mean reaction time differs among the single types. What characteristic of this scenario suggests that a one-way analysis of variance A N O V A is appropriate. Awesome. So it appears for this particular prompt we're asked to determine which characteristic of this specific scenario that is portrayed to us by this prompt suggests that a one-way analysis of variance, ANOVA is appropriate. So now that we know what we're ultimately trying to solve for, let's read off our multiple choice answers to see which one might be our final answer. So A is the data involves a single quantitative variable measured across more than two independent groups. B is the data compares two groups only. C is the variable being analyzed is categorical, and D is the groups are dependent on each other. Awesome. So first off, we need to recall a note that a one-way ANOVA is a correct statistical method when the following conditions are met. You have one continuous dependent variable, which is quantitative. You have one categorical independent factor, and you want to compare means across more than 2 groups, and using this information and applying it to our given scenario, let us note that in our given scenario, Firstly, the variable being measured is the reaction time, which I'll call RT for short. So we're focusing our attention on the reaction time, which in this case is quantitative, so I'll use the letter Q for quantitative. So, secondly, that was firstly, so secondly, the group of variable, so once again, our grouping variable is signal type, so we'll call it GV grouping variable is signal type, which I'll call ST for short, which is categorical with three groups, red, yellow, and green. So it has 3 groups. So since the goal is to compare the means of quantitative variable or quantitative variable across more than two independent groups, a one-way ANOVA is appropriate statistical test to use in this particular situation. And because that is the case, our final answer without a doubt has to be multiple choice answer letter A, which once again is the data involves a single quantitative variable measured across more than two independent groups, and that is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

One-Way Analysis of Variance (ANOVA)

Assumptions of ANOVA

Significance Level (α)

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