Hey Pablo,

Cronbach's alpha estimates the amount of "true" score as assessed by a specific instrument (or inversely stated: estimates the amount of error in your measurement). Basically, this is evaluated by "consistency" of items, i.e. checking that all items positively and strongly enough co-variate with each other (a score is "internally" consistent). But, you have better to look for a more formal definition :)

Assumptions

First, check the assumptions: (1) Normality (especially outliers; see Liu & Zumbo, 2007 ); (2) Cardinality; (3) Tau-equvalence (or at least unidimensionality of the scale items, i.e. common latent factor / reflective model).

Regarding he second point, we already know that you have Likert-scales, which are not cardinal but ordinal. Previous studies indicate that if the range of your Likert-scale is less than 5 degrees (e.g. Not at all = 0; Somehow = 1; Yes = 2 having only 3 possible degrees) alpha might be substantially underestimated. If this is your case, use ordinal alpha instead (see Gaderman et al. 2012 attached in this post).

Interpretation

The interpretation of the coefficient (.844 in your case) depends on the context of the study and use, although values above .70 are considered as "appropriate" in general (I would recommend 0.8, but depends on item pool and the instrument).

Please note that alpha does not imply homogenity or unidimensionality and it is sensitive to the number of items in the instrument (the more items the higher alpha, so one can inflate alpha by adding any number of items in the scale, which is not acceptable in all circumstances)

Alternatives

You can also try to estimate Omega, Beta, or Theta. Furthermore, test-retest reliability (by using the same scale twice on the same subjects) is also well-established estimate that also informs about the stability of the "construct" of interest. Finally, parallel forms can be used (two different but substantially equivalent item sets are compared).

Reliability refers to the amount of true variance that can be accounted for by the observed variance in your measure. Several coefficients have been proposed for estimating reliability from internal consistency, alpha being the most popular. An alpha of .844 seems appropriate, but remember: Alpha only makes sense if it is calculated for items that measure the same construct. It would hardly make sense if, for example, you had a multidimensional scale and you tried to compute a general apha without previously proving the existence of a general factor. I'd also suggest you calculate confidence intervals and check whether the lower limit is not too low (≥.60 is generally considered appropriate). I'm attaching a link to a nice calculator for it.

On the other hand, please consider the fact that to use alpha correctly, some assumptions have to be met first. If it is not the case, you should not use coefficient alpha. Dunn et al.'s paper "From alpha to omega" is a very readable introduction I think you'll find helpful.

Data IC.Alfa.SM

In addition to the internal consistency of instrument items, which is the only think Cronbach's measures, you might also concern yourself with consistency of the instrument over time which helps to indicate the stability of the construct you are measuring.

Hey Pablo,

Cronbach's alpha estimates the amount of "true" score as assessed by a specific instrument (or inversely stated: estimates the amount of error in your measurement). Basically, this is evaluated by "consistency" of items, i.e. checking that all items positively and strongly enough co-variate with each other (a score is "internally" consistent). But, you have better to look for a more formal definition :)

Assumptions

First, check the assumptions: (1) Normality (especially outliers; see Liu & Zumbo, 2007 ); (2) Cardinality; (3) Tau-equvalence (or at least unidimensionality of the scale items, i.e. common latent factor / reflective model).

Regarding he second point, we already know that you have Likert-scales, which are not cardinal but ordinal. Previous studies indicate that if the range of your Likert-scale is less than 5 degrees (e.g. Not at all = 0; Somehow = 1; Yes = 2 having only 3 possible degrees) alpha might be substantially underestimated. If this is your case, use ordinal alpha instead (see Gaderman et al. 2012 attached in this post).

Interpretation

The interpretation of the coefficient (.844 in your case) depends on the context of the study and use, although values above .70 are considered as "appropriate" in general (I would recommend 0.8, but depends on item pool and the instrument).

Please note that alpha does not imply homogenity or unidimensionality and it is sensitive to the number of items in the instrument (the more items the higher alpha, so one can inflate alpha by adding any number of items in the scale, which is not acceptable in all circumstances)

Alternatives

You can also try to estimate Omega, Beta, or Theta. Furthermore, test-retest reliability (by using the same scale twice on the same subjects) is also well-established estimate that also informs about the stability of the "construct" of interest. Finally, parallel forms can be used (two different but substantially equivalent item sets are compared).

Internal consistency is one form of reliability. Basically, it is a measure of how well the items on a scale correlate with one another. More technically, it is the proportion of score variance that is "shared" across items, rather than "unique" to individual items or just random error.

Cronbach's alpha is probably the most widely-used measure of internal consistency. And a value of .84 is perfectly respectable, especially if your scale doesn't have many items (alpha will go up as the number of items increases). So in this limited sense, you can safely state that the reliability of your scale is good.

There are, of course, other forms of reliability. No single type of reliability applies to every type of measure, though. If your scale is objectively scored (e.g., a true-false or likert-type scale), then you don't need to worry about inter-rater reliability. But as Peter says, you might (at some point) want to evaluate test-retest reliability (or stability). This is done by administering the same scale to the same people on two separate occasions, then correlating the scores thus obtained. It is important to the extent that what you are measuring is supposed to remain stable over time.

Indeed, Chronbach's alpha helps you measure the internal consistency of one insrument that measures certain variable (or factor), which is composed by several items (consistent among them). As Pablo Valencia mentioned, make sure that all the items you include in the analysis belong to a pre-assumed factor (e.g. Autonomy dimension in Ryff's PWB Scale) through a previous factor analysis for example. If there is an item (or items) which significantly weakens the instrument's internal consistency, this may affect the variable measure's realiability. There are tools such as SPSS that indicate the degree of adequacy of each item related to the variable in regard. You can delete that item from the instrument you are using to measure e.g. Autonomy, and the Chronbach's alpha will increase. This warrants that the results obtained are reliable, independent from the instrument's validity. The minimal acceptable C.Alpha is 0.80. Hope to have been helpful.         

As others have pointed out an alpha of .844 is quite good and should not affect statistical power.

Because coefficient alpha assumes that all items are equally precise in measuring the construct (essentially tau-equivalent; factor loadings are equal across items and errors may vary), it represents a lowest bound estimate for test reliability. One alternative is the less restricted congeneric reliability (ω; factor loadings and errors may vary across the items).  Use confirmatory factor analysis to estimate this.

One of the issues that you need to think about is whether the construct you are measuring can be thought about as a unitary, in which case you expect a high degree of consistency between the items (0.844 is pretty good) or is a complex or general idea (you might say 'fuzzy'), in which case a high degree of internal consistency is not to be expected because the items are heterogeneous. For example, I have an ability test which  deliberately contains as many different types of items as possible, to measure adaptive thinking; the alpha is around 0.5, normally thought of as too low, but exactly what we want in this case (but if it were much lower it would mean we were measuring nothing at all). You can also think of personality and attitude variables that are deliberately vague and general. So don't be obsessed with high alphas - it depends what you are trying to measure. You can generate artificially high alphas by having lots of items that are similar.

Don Munro,

do you refer to the formative model of measurement (as opposed to the reflective model, on which alpha is based)? If not, could you please provide some reference for it? Generally, how is the reliability conceptualized in such "fuzzy" models? (since we still need how much "error" is in our measurements, right?).

Thank you,

M.

ALPHA  of Cronbach dépend only of the mean correlation between the items of a test....that is ti-o say the internal consistency....one should always prefer if possible test retest reliability.

alpha cronbach's has mean that the scale had general factor

Alpha is a measure foir internal consistency (mean inter-item correlation) of a trest in proportion to test length. In longer tests, a high apha can spuriously suggest a high internal consistency; in shorter ones, a mediocre alpha can spuriously suggest a low internal consistency. See, the annexe.

On the other hand, high alphas in short tests may be there at the expense of the broadness of the concept to be measured. I think, mean inter-item correlation is a better measure of internal consistency than alpha, but it should be evaluated with a look at test length.

i have read all the answers from the experts, that give me alot of information, but i have a tiny question. reliability can be measure with alpha but how about validity ? can we say reliability is good so it is valid too?

thank you in advance

regard

haider

Peter Prudon Adham aa Mahmoud Moussa Francis Pierre Gendre Dawn P. Flanagan Rhonda C Boyd Simon B. Sherry

Hi Arsalan.

Reliability and validity have a connection, but it is pretty much one way...

Validity includes different forms if defining the relevance of the study (internal validity, including construct validity, meaning- does the study neasure what we want to measure?; External validity-testing how it's implementation refers to situations other than the "lab setting", etc.)

In order to have high validity, the study must have high reliability, otherwise it doesn't really test what we want to test.

But, even if the test is reliable, and has high consistency, it doesn't mean that I am actually testing what I think I'm testing. For example, if I try to prime emotions of sadness, I might might actually be priming anger, or not priming any emotion at all....

Or I might be testing something that is valid for lab settings when tested on college students, but not at all valid for larger, more diverse groups (a common caveat with many psychology studies).

So, to sum things up, if there is low reliability, there is low validity, but not vice versa.

Validity need an outside critéria and is generally measure by a correlation coefficient, and so you have many kind of valdity ....Validity is related to reliability but loosey and you cannot say that if something is reliable it is also valid...Reliability is necessary for validity but not sufficient. it just put a ceiling to validity. In the theory of generality valdity and reliability are considered as the same thing the difference is just to what they generalise : in time for reliability in others things for validity

Francis

Hi Arsalan -

Technically, the reliability of a measure sets an upper limit on its validity. After all, reliability refers to the proportion of the variance in test scores that is "true" as opposed to random "error." So to the extent that a test is random, it cannot be valid. But reliability says nothing as to what the test is actually measuring - only that it is, to some degree, measuring something. So as Yaron and Francis have suggested, you really want some sort of external criterion by which to judge the test's validity for a stated purpose.

That being said, reliability does help to establish validity in most cases. As a rule, we want to establish sound measures of theoretical constructs (intelligence, extraversion, dependency, whatever). Showing that the test we're developing measures something at the expected level of reliability is a step in the right direction. But only a step. The argument for the construct validity of the test is long indeed...