# Demonstrating competency

in Alpha

Q8.1. Interpret the 6 factors based on the questions that load on each factor.

## Factor 1

The reliability of the 13 items is shown, from the above extract, to be very high (very good) because the value of the Chronbach's alpha is given as .921 since any reliability coefficient having values of .70 and above is deemed "satisfactory". The items are probably unidimensional (one-dimensional).

## Factor 2

The reliability of the 11 items (VARIABLES= q25 q8 q37 q9 q20 q1 q16 q24 q45 q41 q3) is also very high as Chronbach's alpha is given as .901 but slightly less reliable than the reliability of the 13 items of factor 1.

## Factor 3

The reliability of the 12 items (VARIABLES= q44 q34 q30 q13 q19 q27 q32 q17 q4 q23 q15 q28) is very high as well as Chronbach's alpha is given as .881 but is slightly less reliable than the reliability of both factors 1 and 2.

## Factor 4

The reliability of the 7 items (VARIABLES= q5 q2 q10 q6 q12 q21 q11) is satisfactory as Chronbach's alpha works out to.825 but is slightly less reliable than the reliability of all the previous factors

## Factor 5

The reliability of the 3 items (VARIABLES= q14 q43 q7) is satisfactory as Chronbach's alpha works out to.762.

## Factor 6

The reliability of the 3 items (VARIABLES= q47 q29 q49) is low as Chronbach's alpha works out to .533. This is lower than the acceptable 070 which is considered satisfactory. It could be that the three data variables are multidimensional.

Q8.2. why did I restrict this to a 6-factor structure?

## SOLUTION:

The formula for calculating Cronbach's alpha is given as:

Where:

N= Number of items

C-bar= Average inter-item covariance

V-bar= Average variance

Thus if you raise the value of N, then, the value of Cronbach's alpha also increases. This is also true if you raise the value of C-bar. Thus increasing the number of factors will also raise the value of Cronbach's alpha.

Q8.3. If I told you the exploratory factor analysis was a 12 factor structure what do you think about the construct validity?

## SOLUTION:

Increasing the factor would mean we filter out the data items that are more related (have a higher correlation coefficient). This would increase the reliability of the results and consequently, though not always, the validity of the data.

Q8.4. Provide the rationale for why reliability of the factor structure will be more appropriate than the split-halves method?

## SOLUTION:

The split-halves method attempts to measure reliability in terms of the consistency of the results. It has the following disadvantages as compared to the factor structure method:

1. The test has to be administered several times to verify consistency;
2. Variations in the test subject as it is sometimes difficult to maintain one form for an extended period of time;
3. Overflow(carryover) problems;
4. Variations of the results each time the test is carried out.

Q8.5. Using the output file RELIABILITY determine the reliability for each factor:

## See attached output file RELIABILITY.DOC

Q8.6. What is a good level of reliability? What factors can influence the alpha levels? (See Nunnally, 1978). What is problematic with the (c) Only highest loading questions reliabilities?

## SOLUTION:

Levels of reliability of .70 and above are generally considered satisfactory since, in most statistical disciplines, they are considered to be sampling data items that are unidimensional. One-dimensional data items will always have high reliability levels. Reliability levels lower than .70 are considered "low" and are considered to be of multidimensional data that have a low correlation coefficient.

Two factors can influence the value of Cronbach's alpha (See formula for calculating Cronbach's alpha in Q 8.2 above):

• Increasing the value of N increases the value of Cronbach's alpha
• Increasing the value of C-bar increases the value of Cronbach's alpha

This is somewhat obvious since if the items you are measuring are highly related (indicated by a high correlation coefficient), then you are probably measuring the same data items over a period of time. Thus the data collected will be highly reliable. This is true for unidirectional data items.

If the data is however multidirectional, then the correlation coefficient is low and thus consequently the value of Cronbach's alpha will be low.

Q8.7. Also the output file provides alpha levels if items were deleted so determine whether the construct validity could be improved. Interpret which items would make your factor better. This would be pilot work and would produce a leaner, meaner survey. Look at questions in terms of positive and negative assignment and also whether there is a negative loading of for the question.

## SOLUTION:

Factor 1 data items (VARIABLES=q50 q35 q40 q42 q46 q48 q36 q39 q33 q31 q22 q26 q18) are the most reliable since they have the highest reliability levels .921. From the output file RELIABILITY.DOC, it is evident that the output would be reliable because the average output for Cronbach's alpha if deleted is also very high with the lowest value being .908

## Research questions

Q8.8. Make sure that you're a priori decisions from Session 7 still stand?

## SOLUTION:

According to statistics, a priori decision is a decision made with respect to previous knowledge about the population. These are that:

1. There will be no differences on attitudes due to gender.
2. There will be no difference on attitudes due to grade level.

From the above discussions and from the reliability values obtained above, it is clear that there are no differences between the capabilities of males from females and also the variations in the results is not affected by the grade of the person tested.

Q8.9. Complete non-parametric analyses for your assigned factor for gender

## SOLUTION:

Parametric analysis is used to make predictions (informed guesses) when we are already aware of the allocations of the existing data items and thus from these values, we can carry out repeated tests using the same sample size.

In this case, we already know that there are no attitudes towards gender and thus, knowing this we carry out random samples of the population, then the outcome will show that gender is not a factor of consideration in making the decision.

Q8.10. Complete the analysis for your assigned factor for grade level. How are you going to analyze the research question related to grade level?

## SOLUTION:

Grade level is not equally distribution as gender. However it is not dependent on gender. Thus, repeated tests of the same size will not be dependent on the grade level of the test subject.

Q8.12. Report an equivalent section of your discussion about these results. Deal with the validity, reliability and results. Depending on your alpha levels explain the meaningfulness of your results. And finally deal with effect size and power issues.

## SOLUTION:

Results can be valid without being reliable. Reliability of results is measured /tested by the value of Cronbach's alpha. The value of Cronbach's alpha of the data collected for the data items in question is very high suggesting the reliability of the data. Reliability implies validity. Increasing the number of samples increases the accuracy of the results thus increasing their reliability.

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