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It would make sense to use ANOVA in your analysis if

a) You don't know what else to do

b) Your count data are ordinal

c) You wish to compare numerical outcomes in several stimuli

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Karol E.
Karol E.Lv8
14 Mar 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

APLIA STATISTICSĀ 

The results of the study are presented in the following data table. All scores are times necessary to complete the paper folding-task, recorded in seconds.Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā Ā 

Noise TypeĀ  Ā  Ā  Ā  Ā  Ā 

Participant Classical Music White Noise Nature Sounds Participant Totals Ā 
A 3.22 3.42 3.46 P=10.10 n= 5
B 3.27 3.31 3.35 P=9.93 k=3
C 3.47 3.93 3.69 P=11.09 N=15
D 3.43 3.91 3.74 P=11.08 G=53.33
E 3.35 4.16 3.82 P=11.33 Ā 
Ā  T = 16.74 T = 18.73 T = 18.06 Ā  Ā 
Ā  SS = 0.0441Ā  SS = 0.5286 S = 0.1575 Ā  Ā 

The three treatments in the experiment define three populations of interest. You use an ANOVA to test the hypothesis that the three population means are equal. Present the results of your analysis in the following ANOVA table by entering the missing df values df and selecting the correct values for the missing SS, MS andĀ  F entries. (Note: For best results, retain at least two additional points throughout your calculations. Depending on the order in whichĀ  you do these calculations and the number of digits you retain, you may find slight rounding differences in the last digit between your answers and the answer choices"

ANOVA

Source SS df MS F
Between treatments Ā  Ā  Ā  Ā 
Within treatments Ā  Ā  0.0609 Ā 
Between subjects Ā  Ā  0.1372 Ā 
Error Ā  Ā  Ā  Ā 
TotalĀ  Ā  14 Ā  Ā 

Ā 

A random sample of soil specimens was taken from a large geographic area. The specimens can be assumed to be independent. The amount of organic matter, as a percent, was determined for each specimen. The data are below:
0.14, 0.32, 1.17, 1.45, 3.5, 5.02, 5.09, 5.22
A soil scientist wants to know whether the population mean percent organic matter is different than 4%. A
significance level of Ī± = 0.05 is chosen.

    1. (a) Ā State hypotheses appropriate to the research question.
    2. (b) Ā Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?
    3. (c) Ā Regardless of your conclusion from (b), use the bootstrap to perform a test of the hypotheses you stated in (a). Use B = 8000 resamplings. Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?
    4. (d) Ā Regardless of your conclusion from part (b), use a T -test to perform a test of the hypotheses you stated in (a). Compute the p-value, and make a reject or not reject conclusion. Then state the conclusion in the context of the problem. In other words, does it seem the mean organic matter level is different than 4%?. (I recommend doing this part with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.)
    5. (e) Ā Compare your answers from parts (c) and (d). Which method do you think is better? Are you surprised at the similarity or dissimilarity? What do you think explains this?

Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.

The students receive the following arithmetic test scores:

Ā  Cola Black Tea Coffee Ā 
Caffeine Content (mg/oz) 2.9 5.9 13.4 Ā 
Ā  85 85 92 āˆ‘X2 = 147,641
Ā  86 89 87 G = 1,755
Ā  82 82 80 N = 21
Ā  75 75 89 k = 3
Ā  66 88 96 Ā 
Ā  78 76 83 Ā 
Ā  87 82 92 Ā 
Ā  T1 = 559 T2 = 559 T3 = 559 Ā 
Ā  SS1 = 338.86 SS2 = 338.86 SS3 = 338.86 Ā 
Ā  n1 = 7 n2 = 7 n3 = 7 Ā 
Ā  M1 = 79.8571 M2 = 79.8571 M3 = 79.8571 Ā 

1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?

(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.

(b) The population mean test scores for all three treatments are equal.

(c) The population mean test scores for all three treatments are different.

(d) The population mean test scores for all three treatments are not all equal.

Ā 

2.) Calculate the degrees of freedom and the variances for the following ANOVA table:

Source SS df MS
Between - - -
Within 702.28 - -
Total 973.14 - Ā 

Ā 

The formula for the F-ratio is:

Ā 

Ā 

3.) Using words, the formula of the F-ratio can be written as:

Ā 

Ā 

4.) Using the data from the ANOVA table given, the F-ratio can be written as:

Ā 

5.) Calculate for F-ratio:

Ā 

Ā 

6.)Ā At the level of significance, what is your conclusion?

(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.

(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(d)You can reject the null hypothesis; caffeine does appear to affect test performance.

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