The standard error of coefficient alpha was based on model and distributional assumptions, errors for coefficient alpha obtained using these results were not sufficiently accurate when model assumptions were violated, the items were not strictly parallel. The lack of robustness of the standard errors for coefficient alpha to violations of model assumptions may have hindered the widespread use of hypothesis tests for alpha in applications.

The asymptotic method provided more and factual errors than the duhachek and Iacobucci code method which was used to derive in 2004 to compute the errors, the asymptotic and the traditional theory. This provided a larger sample and distribution of sample coefficient alpha without model assumption. This approach was made by Zyl who assumed only the items composing the test were typically distributed and their covariance matrix is definite thus the best in errors as compared to the code which was used to compute the mistakes.

Q1 Describe at least three (3) different situations these researchers used to test their hypotheses.

Hypothesis tests of whether coefficient alpha equals a prespecified value

This is a hypothesis involving single sample coefficient alpha. This arises when testing whether the population alpha exceeds some predetermined cutoff value. The coefficient is a population parameter which is unknown. The researchers used a structural modeling framework (SEM). They also used the standard errors of sample alpha. Duhachek and Iacobucci provided code in 2004 which was used to compute the errors. They used different test starting with the coefficient alpha based on the results of van Zyl et al. (2000) and Yuan et al. (2003).

They carried out a test whether coefficient alpha equals some a priori value which was any number either 6 or 7. The null and alternative hypothesis was made in comparison with the model-free and asymptotically distribution-free (ADF) which was proposed by Guarnaccia, and Hayslip (2003). SEM packages that have the capabilities for defining the additional parameters which are the functions of the parameters of the model. Plus, version 5 is used (Munchen and muthen 2008) they provided plus input files as supplementary material.

This equation appears in the computer output as the ratio of the estimated alpha difference divided by its standard error. Followed along with its associated p-value... the alternative is one-tailed, the two-tailed value of pin the computer output should be shared by two to obtain the required amount of the one-tailed value of two. When in step one a fully saturated model is used then there are zero degrees of freedom, this led to the model to fit perfectly. The parameters in step two do not introduce the additional constraints on the model.

Different estimates can estimate parameters. This includes the generalized least square estimation (GLS), maximum likelihood estimation (ML) and finally the weighted least square estimation. Under reasonable assumptions, GLS and ML can be used with the standard errors of the asymptomatic distribution free. WLS assumptions assume the ADF. All the estimators lead to the same estimate due to a full model being fitted for coefficient alpha. When estimating the model GLS and the ML lead to the same standard error. When calculating the model without normality assumptions, all the estimates lead to the same standard error. GLS and ML denote GLS and ML estimation. Usual mistakes with ML is performed by the MLM or MLMV which will come to the corresponding parameter estimates and standard errors

Hypothesis tests involving two statistically independent sample alphas as may arise when testing the equality of coefficient alpha across groups

This occurs when comparing the population alpha across two independent samples. When the researcher is interested in examining coefficient alpha in two populations. For example, distinguishing between the female and the male subjects, or in two disjoint samples from the same population. This is actually for testing alpha between the two variables. The alpha coefficients are indicated by population one and two respectively in the population.

When using the structural modeling frame work (SEM) then it is extended to the two populations. The first step is that for each population one is supposed to specify the model to be a p*p symmetric matrix. Then one is supposed to define the three additional parameters in the equation than when the model fits perfectly and the equation gives the statistics then it appears in the Mplus output as the ratio of the estimated alpha difference divided by its error and the value of the two-tailed value of and the confidence interval for the alpha difference may be requested in the process.

Hypothesis tests involving two statistically dependent sample alphas as may arise when testing the equality of alpha across time or when testing the equality of alpha for two test scores within the same sample.

This arises when comparing the population alpha for the two sets of items in a single sample. This is actually when you are testing the equality of the population alpha when an item has been dropped. Testing the quality to a full and reduced scale score. Testing the equality of alpha for the same score measured at the two points. When one is having the code of the normal theory of the standard errors provided in 2004 by duhachek and Iacobucci when testing the equality of alpha across the two populations than the fact that a1 and a2 is equal to the sum of the variances of each sample alpha. The variance of the difference between a1 and a2 depends on the covariance between the two samples alpha. This because they are obtained from the same sample. When two test scores are computed on the same sample of respondents, then it may occur as a product of two test scores being compared are alternate forms of the same test. The first test score is based on p1 items and the second is based on p2 items, while some items may appear on both test scores.

When testing a hypothesis, the difference involving alpha is similar. One has to specify the model to be a p*p symmetric matrix then define the additional parameters for each test scorey11, y21 and a1 for the first test score and y12, y22 and a2 for the second.

No constraints are imposed on the p items. Then the model fits well and perfect. The z statistic is given by the equation five appears in the Mplus output as the ratio of the estimated alpha difference divided by its standard error with the desired two individual values of p.

Q2 Discuss why the authors attribute the assumptions of normal and asymptotically

Distributions.

The normal and the asymptotic distribution free method uniformly outperformed competing procedures across all conditions. The initial proposal for the estimating the standard error of the coefficient alpha was just based on the model and distribution assumptions. It was derived by Kristoff in 1963 who assumed that the test items were strictly parallel. Barchard and Pakistan in 1997 found that the standard error obtained by the method was not accurate. The items were not strictly parallel. Asymptotic was derived in 2000 which was a large sample, and it was the distribution of sample coefficient alpha without model assumptions. Van Zyl et al. assumed that the items composing the test were always normally distributed and the covariance matrix is positively definitive. This approach is model free. The normal theory and asymptomatic distribution free uniformly out

Journal article on coefficient alpha

Medical experts use this method to create questionnaires have reliable and accurate tests. This is just to improve the accuracy of assessment. Reliability is a fundamental key while evaluating a measurement instrument. Calculating alpha is a common practice in the medical research education. This is actually when multiple-item measures of a concept are employed. This method is easier to use in comparison with other estimates. For example, test-retest reliability estimate. This only requires only one test administration.

Alpha was developed in 1951 by lee Cronbach to give an actual measure of the internal consistency of a scale. This describes the extent towards which all the items in a certain test measure the same concept. This method is the best in evaluating the assessments and the questionnaires. It is an employed index in test reliability. It is usually affected by the dimensionality and the text length. Low alpha looks as if the assumptions are not met.

Why Streiner cautions the use and Interpretation of Cronbachs Alpha.

Despite being one of the most commonly used measures on the reliability scale, Cronbachs coefficient alpha is subject to some errors that result to various inconsistencies and hence must be interpreted with some degree of caution.

It cannot be assumed that published estimates of alpha apply in all cases. If the group for which the scale will be used is sufficiently different than the one in the published report, then a will most likely be different. This, therefore, calls for a fresh research due to the change in the composition of the population.

In addition, just because a is affected by the length of the scale, high values do not guarantee internal consistency or unidimensionality. Scales over 20 items or so will have acceptable values of a, even though they may consist of two or three orthogonal dimensions. It is thus essential to carry out an examination of the matrix of correlations of the individual items and to look at the item-total correlations. This prompted to Clark and Watson (1995) recommend a mean inter-item correlation within the range of .15 to .20 for scales that measure broad characteristics and between .40 to .50 for those tapping narrower ones.

Finally, it is evident that alpha is highly sensitive to the number of items in a test. A more substantial number of items in test results to a more substantial number of alpha whereas a smaller number of items returns a smaller alpha. A low value of alpha may mean that there arent enough questions on the test. Adding more relevant items on the test can increase alpha which implies better accuracy since the higher the number of alpha, the more accurate it is likely to be. However, higher values of alpha (over 0.90) may imply unnecessary duplication of content across items and point more to redundancy than homogeneity.

Myths that Underlie Use of Cronbachs Alpha by Researchers.

Alpha is a Fixed Property of a Scale

This myth presupposes that once alpha is determined by one study, then the reliability of the results will be consistent will be consistent with all the subsequent studies. However, this myth has been refuted by some authors based on the fact that reliability is a characteristic of the test scores and not the test itself. This means that the extend of reliability is fully dependent on the sample being tested as on the test.

The guidelines for publishing results of studies (Wilkinson & The Task Force on Statistical Inference, 1999) also emphasize that reliability is a property of the test scores on a test for a particular population of examinees thus a test cannot be labelled as reliable or unreliable, but the test scores can be labelled as such. The reasons for these inconsistencies can be derived from several equations;

The first equation suggests that reliability is the ratio of the variances of the true score to total score. However, another equation shows that the true score is the difference between of the total score and the scoring error from which the true score is often a random with a mean of zero. Consequently, the true score is impossible to obtain since every scale has some degree of error.

Finally, the fact that reliability depends on the total score variance which varies from one sample popul...

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