# Thread: Cronbach Alpha vs Pearson r

1. ## Re: Cronbach Alpha vs Pearson r

Originally Posted by DaniellaS
wouldn't it be meaningful to use the Spearman r instead of the Perason r to compute the Cronbach alpha?
Spearman's rho doesn't translate as easily as the ratio of variance explained to total variance like Pearson's r does. keep in mind that the Spearman assumes a rank transformation of continuous data.

the more correct way to approach reliability for ordinal data from a factor analytic point of view (like Cronbach's alpha does) is by using the matrix of tetrachoric or polychoric correlations to calculate alpha.

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GretaGarbo (10-07-2014)

3. ## Re: Cronbach Alpha vs Pearson r

I think I came up with a better way to measure internal consistency reliability based on L-comoment theory i.e.the L-correlation, which is a hybrid between the Pearson and Spearmen correlations......see here:

http://www.google.com/url?sa=t&rct=j...76943099,d.aWw

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GretaGarbo (10-07-2014)

5. ## Re: Cronbach Alpha vs Pearson r

Originally Posted by noetsi
They are used for different things in different fields. Pearson's looks at the correlation between interval data, regardless of what it is. Cronbach Alpha (commonly used in psychology and education) is really geared to whether raters are consistant among themself in the way they code data although it can get at reliability more generally.
Hi, I'm still a little bit confused here.

I know I can do Pearson's correlation among all the items, regardless of what it is, BUT, In the reality, it is less possible that I correlate for example several statements with length of last name toghter. I could just and only put certain varibales (XYZ) in to the correlation analysis. If I were running a cronbach alpha analysis, I would also put the varibales XYZ in the analysis.

Could I say, If XYZ are all well correlated with each other, they are consistent?

6. ## Re: Cronbach Alpha vs Pearson r

Originally Posted by yue86231
If XYZ are all well correlated with each other, they are consistent?
define 'consistency' please. when you say 'consistency' are you implying it from a reliability/classical test theory perspective? 'consistency' has many definitions within mathematics/statistics and these definitions do not necessarily imply each other.

7. ## Re: Cronbach Alpha vs Pearson r

"Cronbach's alpha is a measure of internal consistency, that is, how closely related a set of items are as a group. "
http://www.ats.ucla.edu/stat/spss/faq/alpha.html

From my understanding of the defination from the above sentence, Cronbach's Alpha means how highly correlated the items are (with each other).

So I can not understand, why we can't just run a correlation among XYZ? It tells how highly correlated with each other.

8. ## Re: Cronbach Alpha vs Pearson r

A better measure of internal-consistency reliability (Cronbach's Alpha) is based on L-moment/comoment theory - especially when distributions are heavy-tailed. See here:

http://opensiuc.lib.siu.edu/cgi/view...text=epse_pubs

9. ## Re: Cronbach Alpha vs Pearson r

Originally Posted by yue86231
So I can not understand, why we can't just run a correlation among XYZ? It tells how highly correlated with each other.
ok, so we're still talking about consistency from a reliability/classical test theory point of view. sorry, your comment about "statements" and "length of last names" threw me off.

if you look at the formula for (standardized) cronbach's alpha you will see alpha is a function of the inter-correlations among items. so yes, you are right. the higher the correlations among the items the higher alpha will be. but alpha gives you more information that correlations by themselves cannot. alpha was developed within a psychometric framework. we usually want to make statements about the reliability of a composite scores (that is usually some weighted sum of the item scores). alpha tells you about the reliability of the scale or test as a whole, whereas each correlation tells you about the reliability of each item individually. it's also important to keep in mind that you rarely have tests with only 3 items (XYZ). they're usually 10, 20, 30 or more. eventually when you look at a 30X30 correlation matrix it can be too much information to process. alpha provides a very consistent summary of it.

if you're interested in just looking at the reliability of each item by itself, then the Classical Test Theory approach is, indeed, correlations of various types. the most common one is the correlation-if-item-deleted (where you correlate the scores on each item with the total score calculated without the item you're investigating so you reduce redundant variance)

10. ## Re: Cronbach Alpha vs Pearson r

Hi spunky, thank you for your detailed explaination, what I have understund is (correct me if I were wrong):
1. correlation : item to item
2. Cronbach alpha: summary of all the correlations between all items.

Now I have a quetion to the number of items , in my study about ad effect,

I would like to ensure that somebody is an option leader , I will use it as a split in further analyses. There are 3 (yes only 3) items:
a1. My friends ask for my option when they are buying digital products
a2. I aks my friend for their option when I am buying digital products.
a3. I post posts about diginal products in social medial.

My professor said to me, that I should run a Cronbach's alpha test here.

Actually what I was planning is just a correlation, if someone gets a high score in a1, then he might also get a high score in a3. (If result is not siginicant, I could tell the retails that they need to do something to improve people's activity in social media and so on, it has nothing to do with questions like a1.)

So right now I am quite confused, should I do a Cronbach's alpha test or not ?? I have made thoughts and choose these three and only three items .

I mean if the result is very low, I need to delete one item, for example, a3, but hey, I am still planning to do something with a3.

And similar with another block in my study:

b1. While watching the ad, I felt excited.
b2. While watching the ad, I fand the ad vivid.
b3. While watching the ad, there were too much information for me.

and at the end of my questionair, I would ask
b4. How do you like the ad?

with b1 , b2 and b3 I am intent to test the reaction of only emotional, emotional + cognitive and only cognitive.
and I would like to run a regression b4 ~ b1 + b2+ b3

If I run a Cronbach Alpha test and have to delete one variable, then my structure is not complete anymore.

So I really could not understand why we should do Cronbach Alpha test and destroy the structure of the questionair....

11. ## Re: Cronbach Alpha vs Pearson r

Originally Posted by yue86231
Hi spunky, thank you for your detailed explaination, what I have understund is (correct me if I were wrong):
1. correlation : item to item
2. Cronbach alpha: summary of all the correlations between all items.
i would say that's a good pragmatic way to understand alpha, yup.

Originally Posted by yue86231
Now I have a quetion to the number of items , in my study about ad effect,

I would like to ensure that somebody is an option leader , I will use it as a split in further analyses. There are 3 (yes only 3) items:
a1. My friends ask for my option when they are buying digital products
a2. I aks my friend for their option when I am buying digital products.
a3. I post posts about diginal products in social medial.

My professor said to me, that I should run a Cronbach's alpha test here.

Actually what I was planning is just a correlation, if someone gets a high score in a1, then he might also get a high score in a3. (If result is not siginicant, I could tell the retails that they need to do something to improve people's activity in social media and so on, it has nothing to do with questions like a1.)

So right now I am quite confused, should I do a Cronbach's alpha test or not ?? I have made thoughts and choose these three and only three items .

I mean if the result is very low, I need to delete one item, for example, a3, but hey, I am still planning to do something with a3.
i don't see any problem with both running inter-item correlations and alpha. besides, alpha would tell you a good summary statistic whether the three items hang well together or not. correlations can only tell you how good they are in pairs but not 3 at the same time. plus, as i said, you cannot make claims about the reliability of your 3-item scale just by looking at the correlations. you would need alpha for that.

besides, obtaining cronbach's alpha is so easy that i don't think it would hurt you to just include it.

Originally Posted by yue86231
And similar with another block in my study:

b1. While watching the ad, I felt excited.
b2. While watching the ad, I fand the ad vivid.
b3. While watching the ad, there were too much information for me.

and at the end of my questionair, I would ask
b4. How do you like the ad?

with b1 , b2 and b3 I am intent to test the reaction of only emotional, emotional + cognitive and only cognitive.
and I would like to run a regression b4 ~ b1 + b2+ b3

If I run a Cronbach Alpha test and have to delete one variable, then my structure is not complete anymore.

So I really could not understand why we should do Cronbach Alpha test and destroy the structure of the questionair....
i have absolutely no clue of what you mean by having to delete one variable and influence the structure of your test. that doesn't really make sense to me. you don't need to delete anything to calculate Cronbach's alpha.

12. ## Re: Cronbach Alpha vs Pearson r

i have absolutely no clue of what you mean by having to delete one variable and influence the structure of your test. that doesn't really make sense to me. you don't need to delete anything to calculate Cronbach's alpha.

Hi, thank you for your reply. What I meant is:
I have 3 items intitially
run Cronbach's alpha check --> under 0.7
have to delete 1item

I read about removing items here: https://statistics.laerd.com/spss-tu...statistics.php

last two paragragh
"This column presents the value that Cronbach's alpha would be if that particular item was deleted from the scale. ....."

So according to my understanding, we test the Cronbach Alpha in pilot test, if the Cronbach Alpha is under 0.7, then you need to remove some "bad" items . So my concern is, I have only 3 items which check different dimentions of my quesion, it could be really annoying if I have to remove them due to low Cronbach Alpah.

13. ## Re: Cronbach Alpha vs Pearson r

well, let's unpack a few things here.

for starters, there is absolutely no consensus as far as when an item has to be deleted if a certain alpha "threshold" is crossed or not. all these rules of thumbs or guidelines can be questioned because statistics is not a 'one-size-fits-all' endeavour.

the way this whole "let's delete items" thing works usually has in mind that you have more than 3 items. whenever you're working with a pilot scale, you usually want a lot of items because you're going to throw out a few. a professor i know usually said one should develop scales with 3 times more items than you had in mind initially because chances are you're going to throw out 2/3rd's of them. if in your case you only have 3 items and you don't feel like they need to be removed, then don't remove them and that's it. your scale doesn't fit this model of having lots of items from which you get to remove all the ones that don't work optimally. if your cronbach's alpha is bad it's probably because you only have very few items, so i doubt dropping one of them would make things substantially better. although, to be honest, if you had a cronbach's alpha of say 0.5 with 3 items that jumped to 0.9 if you dropped one item, i would probably drop it. but unless the gain on alpha is dramatic, i would keep them all.

there are no hard, iron-clad rules here. test construction and validation is a "play-it-by-ear" kinda thing until you develop the experience to create good tests.

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