Assignment: Calculation of ANOVA

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Assignment: Calculation of ANOVA

Assignment: Calculation of ANOVA

Instructions- Calculate this ANOVA by hand.  Check your work by also calculating the ANOVA in SPSS or EXCEL.  Be sure to do any multiple comparison tests and interpret the results.

 

Control GroupA1 PsychoanalysisA2 CBTA3
X1 7 7 3
X2 10 5 3
X3 6 6 2
X4 8 5 3
X5 10 5 4
X6 10 6 2
X barA1
SX (A1)
SX2

 

SST = SX2 – T2/an                             (also called [X] – [T])

 

SST =                                                  (a = number of groups, n = number in each group)

 

 

SST =

 

 

 

SSA = SA2–   T2                                 (also called  [A] – [T])

n        an

 

SSA =

 

 

SSA =

 

 

SSS/A = SX2 – SA2                                        (also called [Y] – [A] )

N

 

SSS/A =

 

Now divide by its df to change it to variance.  Variance is called Mean Square.

Complete ANOVA summary table on next page.

 

ANOVA Summary Table

Source                                   SS                   df                     MS                  F

A-group

S/A (error)

Total

 

 

Find F-critical.

 

Permalink:

 

Are the groups significantly different?

 

 

 

Write the results statistically.

 

 

 

What do you do next?  Why?

 

 

 

 

Which groups are different?

Week 2 Visual Perception Discussion

Your group will facilitate a class discussion on the role of attention in visual perception.

Create a discussion guide that includes 8 to 10 open-ended questions that will help facilitate the discussion. Include the desired responses.

Explain the concept of inattentional blindness and how this can affect visual perception

Provide an example and visual aids.

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator’s belief about the population parameters. The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable in two or more independent comparison groups. For example, in some clinical trials there are more than two comparison groups. In a clinical trial to evaluate a new medication for asthma, investigators might compare an experimental medication to a placebo and to a standard treatment (i.e., a medication currently being used). In an observational study such as the Framingham Heart Study, it might be of interest to compare mean blood pressure or mean cholesterol levels in persons who are underweight, normal weight, overweight and obese.

The technique to test for a difference in more than two independent means is an extension of the two independent samples procedure discussed previously which applies when there are exactly two independent comparison groups. The ANOVA technique applies when there are two or more than two independent groups. The ANOVA procedure is used to compare the means of the comparison groups and is conducted using the same five step approach used in the scenarios discussed in previous sections. Because there are more than two groups, however, the computation of the test statistic is more involved. The test statistic must take into account the sample sizes, sample means and sample standard deviations in each of the comparison groups.

If one is examining the means observed among, say three groups, it might be tempting to perform three separate group to group comparisons, but this approach is incorrect because each of these comparisons fails to take into account the total data, and it increases the likelihood of incorrectly concluding that there are statistically significate differences, since each comparison adds to the probability of a type I error. Analysis of variance avoids these problemss by asking a more global question, i.e., whether there are significant differences among the groups, without addressing differences between any two groups in particular (although there are additional tests that can do this if the analysis of variance indicates that there are differences among the groups).

The fundamental strategy of ANOVA is to systematically examine variability within groups being compared and also examine variability among the groups being compared.

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