Cronbach’s Alpha is the most commonly used statistic for determining the internal consistency of measurements, such as items in a questionnaire, exam, or survey. It is equivalent to performing the split-half methodology on all combinations of these items.
Topics
- Basic Concepts
- Real Statistics Support
- Hypothesis Testing and Confidence Intervals
- Power and Sample Size
- Handling Missing Data and Not Applicable Entries
- Proof of Main Property
References
Tavakol, M., Dennick, R. (2011) Making sense of Cronbach’s alpha. International Journal of Medical Education
https://www.ijme.net/archive/2/cronbachs-alpha.pdf
Gliem, J. A., Gliem, R. R. (2004) Calculating, interpreting, and reporting Cronbach’s alpha reliability coefficient for Likert-type scales
https://scholarworks.indianapolis.iu.edu/server/api/core/bitstreams/976cec6a-914f-4e49-84b2-f658d5b26ff9/content
Newsom, J. (2017) Empirical estimates of reliability: Cronbach’s alpha
https://web.pdx.edu/~newsomj/pmclass/empirical%20estimates%20of%20reliability.pdf
Trizano-Hermosilla, I., Alvarado, J. M. (2016) Best alternatives to Cronbach’s alpha reliability in realistic conditions: congeneric and asymmetrical measurements
https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2016.00769/full
Thank you, thank you, thank you for this clear and logical explanation of how to apply Cronbach’s Alpha to a Likert scale.
Hi I have another query to add to this. I have run the Cronbach’s alpha for 2 of the individual manager’s sets of results for one of the scales and a set of data I would have thought should have shown far lower inter correlation than the other came out the other way round. Is it because I only have about 6 individuals results – which is too low?
Yvonne,
It is difficult to answer your question without seeing the data, but as I said in my previous response it doesn’t sound like Cronbach’s alpha is the correct measurement to use in any case.
Charles
Hi firstly thank you so much for this website it has been so helpful. I am doing an MSc just now and am looking at manager’s self-awareness and how closely their followers/direct reports assessment of their leadership styles agree. I have only 7 managers and 26 direct reports results.
I have a few queries from when I apply Cronbach’s alpha – should I be looking at the manager and their direct reports results as individual cronbach’s alpha? Or can I combine all the data as one set of 33 results? Also when I first ran Cronbach alpha on the 6 questions which made up one scale, I got a figure of >1. I worked out this was because the missing data points must be being used as 0s. I first excluded the whole column of data (ie 3 of the criteria for the scale) and got a figure, then I ran it again removing the people with the missing data – and got a similar figure to that of removing the question. Which is correct way of doing this? or how else should I deal with missing data? Also, looking at an earlier response Cronbach’s alpha may not be very accurate/reliable with such a small sample? Any other ideas of how I could analyse the data? The purpose of my MSc question was to discover if the manager’s view of their leadership style matched that of their direct reports. So possibly I do need to do cronbach’s alpha on each manager – rather than using it as one data set?
Charles,
I have done the split-half methodology against our set of multiple-choice questions; and thus far, the results look good. Since students may not get the same question (although all questions measure the same concept(s)) on their specific exam, I had to sample each conceptual question into groups of 30.
For example, I would have thousand rows with the columns of NumQuestionOffered=30, and NumQuestionCorrect=X
Provided I have the Odd/Even Anlysis Means, StdDevs, etc. ..is it possible to use that data to produce a standardized Cronbach’s Alpha?
Sorry Martin, but I don’t completely understand what you are trying to do. I see that you are trying to combine questions, but I don’t understand how the split half accomplishes this.
Charles
I have 6 items with SA, A, SD, D, how do I apply cronbach alpha with these figures.
Udo,
Just assign the values 4 to SA, 3 to A, 2 to D and 1 to SD and use the approach described in the referenced webpage.
Charles
Thanks for the great resource pack and website. My question: While using Fleiss’ Kappa to measure rater agreement, I experimented with various agreement scenarios but now have trouble interpreting the kappa. With 11 subjects and 5 raters on a 5 point scale, I set everyone’s agreement on the middle of the scale (e.g., 3 on a 1 to 5 scale). Kappa would not calculate until I moved 1 score into another column. So, with all raters=3 for all subjects except one, kappa calculated to -0.01852. Intuitively, I expected a number close to 1. I’m left wondering if the answer is 1 minus the calculation.
I appreciate your help.
What Statistical tool can best be used to test hypothesis of significant INFLUENCE of one variable over the other. the two variables have separate instruments measuring them. Is it T-test, Correlation, Regression, Chi-square, or which
Thanks
Influencers is a term used in association with residuals in regression. See the webpage https://real-statistics.com/multiple-regression/outliers-and-influencers/ for more details.
Charles
good afternoon sir. I am conducting a comparative study to assess the developmental milestones of children in rural and urban areas. I am using checklist as a tool. My tool have three categories 6 years,7 years,8 years. Each categories has different questions. 6 years contain 6 question. 7 years category contain 7 questions. 8 years category contains 7 question. I want to check the reliability of tool. Than how I will check the reliability of tool
Good afternoon sir.
my tool is checklist. It has three catageries 6 Year(1 catg),7 Year(2catg),8 year(3 catg). 1 catg contains 6 items,2 catg and 3 catg contains 7 items. How i will calculate reliability.
thank you
Sona,
Unfortunately, you haven’t provided enough information for me to make any recommendations.
Charles
This a great websites I have gone through several books and websites nowhere I got all these information My sincere respect to you.
Regards
Shiba
Asst Prof
Shiba,
I am very pleased that you find the website valuable. I am trying to create an easy-to-use, yet powerful resource that is available to everyone who needs to learn, teach or use statistics.
Charles
There are typos in your equations for x_0 and t_0. You should be summing over x_j and t_j (i.e.: $x_0 = /sum_{j=1}^k x_j$ and $t_0 = /sum_{j=1}^k t_j$), respectively.
Lou,
Thanks for identifying these typos. These sorts of mistakes can really cause confusion for people who are less familiar with the notation, and so I really appreciate your comment. I have now made both corrections.
Charles.
Charles:
I am conducting multi-variable regression using 5 independent variables to predict the impact on transportation costs as a proportion of income in 75 metropolitan statistical areas. The data includes employment rates, population density, and value of exports. Is Chronbach’s Alpha an appropriate test for reliability or should I be using a different type of test? If is is appropriate, should I be including the dependent variable in the calculation? Thank you very much.
Reggie,
I can’t see why you would want to use Cronbach’s alpha in this case. What is the objective of the reliability test you want to pperform?
Charles
Charles, thank you so much for this article; it is very helpful for a math novice like myself. I would be grateful if you could assist me with some questions regarding the calculation of the Cronbach Alpha.
We have a test which deals in direct assessment. To be brief, I would like to calculate the reliability of our testbank broken down into topical groups. While our testbank will contain about 300-400 questions per topic alone, each student is only presented with 10 random questions. I have a population of 800. Does it matter if the questions (all multiple choice) are different for each student? Can I still create 10 columns with 800 rows?
My assumption tells me I cannot, because Q1 for student 1 may have gotten it correct, and student 2 and 3 may have also gotten it correct, however, Q1 for student 2 and 3 could be the same, or, most likely entirely different (although all the concepts are the same).
Please advise
I don’t know how to calculate Cronbach’s alpha in this situation.
Charles
hie,
what percentage of respondents do i need when using cronbach alpha during pretest? where can i get this reference. a friend told me that i need 10% of the respondence, is it true please help.
Maggy,
I have seen a number of websites that have information about the minimum sample size for Cronbach’s alpha. I used the following search on google: “minimum sample size for cronbach alpha”
I have also seen the following paper which you may find helpful:
Research in Nursing & Health, 2008, 31, 180–191
Considerations in Determining
Sample Size for Pilot Studies
Melody A. Hertzog*
Charles
Hi Charles
Thank you very much for the resource you provide.
My question is the following: I usually run alpha on a very limited sub-sample (about 10 cases) before delivering any questionnaire in order to asses the consistency of it; btw I have no reason for choosing this number, 10 cases. Is there any rule suggesting a minimum number of cases or a minimum ratio cases/variables to have a ‘solid’ alpha?
Giacomo
Giacomo,
I have seen a number of websites that have information about the minimum sample size for Cronbach’s alpha. I used the following search on google: “minimum sample size for cronbach alpha”
I have also seen the following paper which you may find helpful:
Research in Nursing & Health, 2008, 31, 180–191
Considerations in Determining
Sample Size for Pilot Studies
Melody A. Hertzog*
Charles
Thank you again!
Cheers
Giacomo
Charles,
First, let me thank you for these excellent tools. They provide wonderful access to statistical results related to educational outcomes.
I run Excel 2010 and have the downloads installed. However, I can run cronalpha, but not with the k switch. Nor can I run calpha. What do you think is missing, misplaced, or uninstalled.
Roy
Roy,
I introduced these capabilities quite recently. If you are using a version of the software prior to Release 3.0 these capabilities are not included. I suggest that you download the latest version of the software.
Charles
i need draw backs of cronbach alpha test.
why cronbach is important for internal consistency?????
Cronbach’s alpha measures internal consistency. Internal consistency is important because it determines whether a questionnaire or some other measuremnt tool is measurin the same thing. If for example you design a questionnaire to determine whether someone is bipolar, you want to make sure that all the questions are measuring the same thing,
Charles
A couple of drawbacks:
– Cronbach’s alpha measures internal consistency, but the more items the higher Conbach’s alpha will be even though the internal consistency isn’t any higher.
– Redundant items (e.g. the same question phrased slightly differently) will increase Cronbach’s alpha
Charles
Dear Charles,
Really hope you can solve my problems.
My questionnaire consist 3 parts which are
1. Knowledge in action research – Using test form (5 multiple choice answers and 5 open-ended questions)
2. Skills in implementing action research – Using 5 point likert scale
3. Attitude towards action research – Using 5 point likert scale
My problem is how to run reliability test for part 1. Because in this part have few difference types of questions.
Example:
1. multiple choice (A , B , C , D )
2. list out 4 data collection techniques
3. pls arrange 10 steps of implementing action research using number 1 to 10.
My friend advise me to run Kuder Richardson, which one more suitable?
If use Kuder Richardson to get reliability for part 1, then how about the overall reliability for the questionnaire? How to run the test?
Anyway thanks a lot.
The multiple choice questions can be coded as 0 for a wrong answer and 1 for a correct answer. You could code the 4 data collection techniques as four questions with 0 for an incorrect technique and 1 for a correct tecnique. I am not sure how you want to code the 10 steps question as right or wrong (this is necessary if you want to use Kuder Richardson).
You can use Cronbach’s Alpha. If all the scores are 0 or 1 the result for Kuder Richardson is the same as for Cronbach’s alpha (the referenced webpage). You can also look at the webpage https://real-statistics.com/reliability/kuder-richardson-formula-20/.
What is most important is that Kuder Richardson (or Cronbach’s alpha) is calculated only from questions that are measuring/testing the same thing.
Charles
Thank you very much for your valued information given above. I really learn a lot. Only I have one question. If I have three different companies answering same questions? Can I measure the internal consistency by conducting Cronbach’s alpha? Even ratters from company A have different circumstances than B or C?
Faisal,
Cronbach’s alpha doesn’t work with only one question, although there are some other procedures for dealing with one question. I gave a link to one of these in a previous comment. I wouldn’t expect much with such a limited amount of data.
Charles
Dear Charles,
Thank you very much for your prompt replay. I mean I would like to ask only one question. I am sorry it was my fault not describes my question very well. I have 10 groups with 43 factors and I have 36 response from three different companies rate my factors. If I have three different companies answering same questions? Can I measure the internal consistency by conducting Cronbach’s alpha? Even ratters from company A have different circumstances than B or C?
Dear Faisal,
Yes, you can use Cronbach’s alpha to create one value of alpha (or three values, one for each company). It would be interesting to see whether you get different values for the three different companies.
Charles
I have a mixed set of questions in my questionnaire where some questions are based on 5 point likert scale and some are single response questions not dichotomous. So, how should I calculate the cronbachs-alpha value for all set of questions in my questionnaire.
Sadhna,
The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.
Regarding your specific request, can you give me some idea of the single response questions that you are using?
Charles
Got your point, thanks. lets say I have question 1. Which parameter do you look for while selecting the service provider?a)call charges b)network availability c)Customer care services d) offer and schemes e) any other. For these types of questions, how to calculate cronbachs alpa value.
please, how do I compute the correlation
between a particular item and the
sum of the rest of the items.
Say the the data is in range A1:F50 and you want the correlation between the data in column E and the sums of the rest of the items. Now place the formula =sum(A1:F1)-E1 in cell G1, highlight range G1:G50 and press Ctrl-D. The result that you are looking for is calculated by the formula =CORREL(E1:E50,G1:G50).
Charles
Dear Charles,
Is it possible to determine the reliability of a survey questionnaire even if there are no established correct answer since it deals with their opinions? Should it be possible, what are the steps in computing it using the spreadsheet?
Riza
Dear Riza,
Yes. E.g. if the answers are in the form of a Likert scale then you could use the Likert scale score to calculate Cronbach’s alpha.
Charles.
.
Hi there,
I have a questionnaire which contains:
1) Yes/No items
2) Likert-scale items
Can I use Cronbach? If yes, how do I perform the coding for 1) & 2) in SPSS?
Appreciate your advice.
Debbie
Hi Debbie,
The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.
I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (did Columbus discover America?).
I don’t use SPSS and so am not familiar with the coding in SPSS. For the Real Statistics Resource Pack you would code a Likert scale of 1 to 5 with the numbers 1 through 5. You would code True/False (as well as multiple choice questions) with 1 for the correct answer and 0 for the incorrect answer.
Charles
Dear Charles,
Thank you so much! Much appreciated.
Debbie
Hello Charles,
I wish to use cronbach to demonstrate some internal consistency of a survey. If this has different sections and the sections each have mixtures of types of questions e.g, likert,dichotomous,multiple choice..how do I test for cronbach please? Thanks
The important thing is to calculate a separate Cronbach alpha for each group of questions that are testing the same thing. Stated the other way around, you shouldn’t calculate Cronbach’s alpha for a set of questions that are testing different things.
In my view there is no problem mixing true/false and multiple choice questions provided the above paragraph is adhered to.
For multiple choice questions of the form “Select one of the following four choices a, b, c or d” if say (c) is the correct choice then use the value 1 if the person selects choice (c) and use the value 0 if the person selects a, b or d.
Questions of the form “Select one or more of the following four choice a, b, c or d”, can be viewed as four True/False questions, namely choice (a) is correct (True or False)?, choice (b) is correct (True or False)?, choice (c) is correct (True or False)? and Choice (d) is correct (True or False)? If say the correct choices are (a) and (d), and a person chooses (a) and (b) instead, then score 1 for question (a), 0 for question (b), 1 for question (c) and 0 for question (d).
I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (in which year did Columbus discover America?).
Charles
Hi, I am currently working on my research. I face problem when i generating Cronbach Alpha. My questionnaire contains such question :
If yes,please answer Section B.
If no, please answer Section C.
It’s quite complicated, how to obtain the Cronbach Alpha value after i key in all?
If answer section B, what i need to fill for section C items? With missing value or without missing value?
Need a guide to complete it as I running out of time.
Kyan,
Perhaps the easiest approach is to calculate Cronbach’s alpha for the questions in section B (ignoring the people who didn’t answer the questions in section B) and calculate a separate Cronbach’s alpha for the questions in section C (ignoring the people who didn’t answer the questions in section C).
Charles
Enriching information.Kudos
What percentage of the population is recommended for purpose of determining Cronbach Alpha?
Joseph,
I have generally used the entire population of subjects who have filled in a questionnaire to calculate Cronbach’s alpha.
Charles
Dear Charles,
I have followed the chat, however, still did not get how to calculate alpha with multiple choice questions.
What do you mean by “correct (1)/incorrect(0)”? For instance, my questionnaire contains some questions, beside of Likert scale questions, with 5 sentences and the respondent is asked to mark those sentences which he associate with the particular subject. That means many different combinations could be marked.
Also there are such questions which require to range 5 sentences from most favourable to least favourable – also the answers could vary alot. How to cope with such questions while calculating alpha?
Thank you very much
Dear Darius,
For multiple choice questions of the form “Select one of the following four choices a, b, c or d” the approach that I suggested should work, namely if say (c) is the correct choice then use the value 1 if the person selects choice (c) and use the value 0 if the person selects a, b or d.
Questions of the form “Select one or more of the following four choice a, b, c or d”, can be viewed as four True/False questions, namely choice (a) is correct (True or False)?, choice (b) is correct (True or False)?, choice (c) is correct (True or False)? and Choice (d) is correct (True or False)? If say the correct choices are (a) and (d), and a person chooses (a) and (b) instead, then score 1 for question (a), 0 for question (b), 1 for question (c) and 0 for question (d).
I am not sure how best to handle questions of the form “List the following five choices from most favourable to least favourable”. They are similar to having five questions where you rate each on a Likert scale of 1 to 5, but the difference is that you can’t use the same Likert score twice. Perhaps someone else has an idea about how to handle these types of questions
Charles
I´ve just discovered Real Statistics, and so far it looks fantastic!
I´m looking to automate lots of calculations on a complex data set.
Is it possible to make the formula only calculate certain questions (for a subscale)?
How does the formula handle missing items/participants?
Kind regards,
Martin
Martin,
Real Statistics has a lot of useful statistical functions and data analysis tools. I am also adding new features all the time.
There are various functions for selecting only certain data from a data range. These consist of standard Excel capabilities (Data > Filter, etc.) and Real Statistics capabilities (e.g. Extracting Columns from a Data Range data analysis tool and ExtractCol function).
Many of the statistical functions ignore any rows with missing data, but the CRONALPHA doesn’t have this capability. You need to first remove any missing data (e,g, by using the Real Statistics function DELROWBLANK or DELROWNonNum or via the Reformatting a Data Range by Rows data analysis tool) and then apply the CRONALPHA function to the reduced data range.
Charles
Just wanted to say what a fantastic resource you have put together here. I’m an educational researcher from a purely Arts background.
I put together a Likert survey, made up of 6 root statements (or factors?), and chose to analyse 3 of them using this method. I had 79 respondents and used a 5 point scale. The first factor consisted of 7 items and the second and third of 4 and 3 respectively. The spreadsheet returned scores .88, .84, and .79. I am well pleased!
I may even have a go at using your site for Factor Analysis and go a step further…
Much, much appreciated.
Chris, New Zealand.
Chris,
I am very pleased that you found the site useful. Interestingly enough the original impetus for creating the site was that I wanted to perform Factor Analysis in Excel. Once I figured out how to do this I decided to share what I had learned with others who might want to do real statistical analysis using Excel.
Charles
Hi Charles, firstly thank you very much for providing this informative platform for everyone. Your effort is greatly appreciated.
Anyway, i do have some issues regarding alpha cronbach. Hoping that you can give me some clarification. Issues are stated as follows;
(i) In one full set of questionnaire, i have 42 items/ questions measuring different and diverse concepts/ factors. In another word, i cannot put all the items together at one go for Cronbach test (as this will lower the cronbach value as they are measuring different things), so i separate them into few groups say 8 groups of factors (consists of 3-5 or 2-3 items). So theoretically, each group i have different value of Cronbach if i executed cronbach for all the items. The question is do i need to execute the cronbach test for ALL items or groups? Is it necessary to ‘cronbach’ all the items? Can i just ‘cronbach’ just one group?
(ii) In exension of above issue, as you mentioned earlier, in order to use Cronbach, you have at least 2 items right? but we know that the lesser the items, the lower alpha cronbach will be. Say i have low cronbach value for 2 items, but these two items are valid to be in questionnaire just the reported reliability is low, so, do i need to do the cronbach test for that group? or i just ignore it? or there is a better alternative?
(iii) For your information, another issue is there are some items, like 2-3 items they are unique (maybe i have to say, they are not ordinal data, they are nominal data- yes or no etc, meaning to say, they are representing individual factor, so cronbach cannot be used right? is there alternative to replace the cronbach if this is the case? One more issue is multiple choices questions, i have about 8 of them, so, how can i establish reliability of them, is that possible?
Thank you very much
Gabriel,
(i) You only need to calculate Cronbach’s alpha for the group(s) you are interested in.
(ii) As you know, all other things being equal, in general the more questions you have the higher the value of Cronbach’s alpha will be. For this reason the value of Cronbach’s alpha for two items (i.e. two questions) might seem low compared to a group with more items. There may be better alternatives to Cronbach’s alpha for two items, but I am not aware of them.
(iii) Cronbach’s alpha handles true/false and multiple choice questions with no problem. You code these with 0 for the wrong answer and 1 for the correct answer (as in Example 1 of the referenced webpage).
Charles
Hi,
for my thesis I conducted CRONBACH alpha on several measures- the core questionnaire is the Five Facet Mindfulness Questionnaire (FFMQ). My sample is 265 Norwegian University students.
These are the scores I need to explain: FFMQ (0,582) where the individual facets never reach even 0.5, for the Perceived Stress questionnaire (0,345) and for AUDIT (0,396).
My supervisor thinks these are too low and would like me to explain why, and thinks we cannot be sure what the instruments were actually measuring. He wants me to give reasons for this.
Also, the CORRELATION between measures was low even though in the past it usually shows to be high. I am not sure what was different now, and what both a low cronbachs alpha and correlation could indicate.
I have found some reasons that could explain it like Participant Fatique.
I would truly appreciate any help as my thesis defence is due very soon and I am still stuck at this problem.
Best,
MJ
MJ,
Since this is a standard test, I assume that your supervisor finds that your results are too different from the typical results for the test. You mention that a possible reason is Participant Fatigue, but you need to ask yourself why would students taking this questionnaire have higher levels of fatigue than the typical respondents to this questionnaire? In general, I can only think of two categories of reasons for the discrepancy: (1) the people taking the test are different from the typical people taking the test (different culture, problems with language, etc.) or the environment where the questionnaire is administered is different (too noisy, poor lighting, etc.) or (2) you aren’t measuring the the same thing as is typically measured — e.g. if I remember correctly the FFMQ has 5 different dimensions (factors), in which case you need to calculate Cronbach’s alpha not on the whole questionnaire but for the questions in each of the five dimensions separately.
Charles
I have multiple choice question with one correct answer
How can i get internal consistancy for my questionnaire, should i use similar method in spss to get chronbach alpha vlue for likert scale for my 15 question of MCQ??
First in coding a b c d with 1.2.3.4
But now..i coding them 1 for correct answer and 0 for uncorrect answer
So what should i do next??
Farah,
When using a Likert scale (such as 1, 2, 3, 4) you should use the appropriate value 1, 2, 3 or 4 for each question, but multiple choice questions are not like questions using a Likert scale. When you are analyzing multiple choice questions you should code 0 (incorrect) and 1 (correct). After the coding just following any of the approaches described on the referenced webpage to obtain Cronbach’s alpha.
Charles
A lot of thank for replied my massage..:)
By the way, what do you mean by following any approaches described on reference webpage to obtain cronbach alpha?
I hv difficulties to analyze my data to get alpha value..
What should i use..anyway..any suggestions?
Farah,
On the referenced page I showed three ways of computing Cronbach’s alpha:
1. Directly using the definition of Cronbach’s alpha (as in Example)
2. Using ANOVA (as in Example 3)
3. Using the CRONALPHA function found in the Real Statistics Resource Pack (as in Example 4)
Charles
Thank you very much charles:)
I still dont understand about why should we change into 6 instead of 2…
N Q20….”Q20 in our example. Thus if a response to Q20 is say 2, it needs to be scored as 6 instead of 2 (i.e. 8 minus the recorded score).”
And why must be 8?
Im very confius…
Hope u can help me…
Thanks
Farah,
Suppose you pose the following four questions and ask your respondents to give a rating of 1 to 7 for each, where 1 is the weakest response and 7 is the strongest response:
“Do you like pie?”, “Do you like steak?”, “Do you like green beans?” and “Do you dislike pizza?”
The fourth question is reverse phrased: “dislike” instead of “like”. A response of 7 to the first question means that the respondent really likes pie, while a response of 7 to the fourth question means that the respondent really dislikes pizza. This last response is equivalent to a response of 1 to the question “Do you like pizza?”. So in order to “compare apples with apples” (pun intended) you pretend that the last question was “Do you like pizza?” and use a score of 1 instead of 7.
In a similar way, a response of 6 to the question “Do you dislike pizza?” is equivalent to a score of 2 to the question “Do you like pizza?” Note that with a Likert scale of 1 to 7, the reverse coded score is always 8 minus the actual score (here 8 is 7+1). Similarly, if the Likert scale is 1 to 5, the reverse coded score is 6 minus the actual score (here 6 is 5+1).
I hope this helps.
Charles
Dear Charles,
as if you have different parts of questionnaire e.g. Yes, No and with 5 scale options.. So would there be two separate evaluations of C Alpha or may i find the one single value as well for both segregated portions of questionnaire ?
Dear Hammad,
Are you saying that if they answer Yes they have to evaluate something on the scale of 1 to 5, while if they say No they have a separate evaluation also using a scale of 1 to 5?
Charles
Hi,
I would like to know, if i have 5 variables that i want to categorize into a single variable. Out of them, 4 questions are likert scale and 1 is a yes/no question. how can i find the chronbach alpha for the 5 questions?
Hi Koel,
Provided all the questions measure the same thing you can calculate one Cronbach’s alpha for all the questions.
However, I would not mix Likert scale questions (rate your opinion of Columbus from 1 to 5) with knowledge questions (did Columbus discover America? T/F).
Generally for the Likert scale questions use the Likert scale (say 1 to 5) in calculating Cronbach’s alpha. For True/False questions you can use values that correspond to the Likert scale (e.g. 5 if True means you have an extremely high opinion of Columbus and 3 if No means that you have neutral opinion). Most of the time True/False questions are measuring knowledge and so as stated above it is not appropriate to mix them with Likert scale questions in calculating Cronbach’s alpha.
In general with knowledge-based questions (e.g. True/False or multiple choice questions) you can code them as 1 for the correct answer and 0 for an incorrect answer when calculating Cronbach’s alpha.
Charles
Charles
Dear Charles,
I have made a series of multiple choice questions with 70 items and gave them to a group of ten for piloting but it is really hard to estimate Cronbach’s alpha. I know that it should be more than 0.7 but I don’t know how. Please help me. Thank you so much in advance.
Sincerely,
Marzieh
Dear Marzieh,
If the person answered the question correctly they score 1 for that question. If they answered it incorrectly they score 0 for that question. Then use the approach in Example 1 of the referenced page or the CRONALPHA formula to calculate Cronbach’s alpha.
Charles
Hi,
I have 4 questions of type Likert Scale ( each of them contain 4 questions describing the main question).
As far I saw that cronbach alpha is for internal consistency, or it shows how good items are related to describe the main question.
I want to measure inter-rater agreement. Is Cronbach Alpha the right metric for doing this?
Thank you
Hi Ermira,
Depending on your specific requirements, you could use Cohen’s kappa, Weighted kappa, Fleiss’s kappa, ICC or Kendall’s W. These all measure inter-rater agreement and are described in the website. See https://real-statistics.com/reliability/ for more details.
Charles
Hello,
Thank you for the explanation and the answers that you gave, it is very helpful !
I hope that you can help me with my problem, since it is more or less specific..
I’m trying to calculate Cronbach’s alpha for a specific purpose: inter-rater reliability (rather than internal consistency reliability) where raters used Liker-scale to judge some behaviors shown in videos. 8 items were used for the Likert-scale. Until now it seems fine, I can measure Cronbach’s alpha coefficient for one behavior (one observed video) while considering 8 rows (for the 8 items) and n columns (for n raters).
However, there are many videos, and each rater evaluated only 16 videos (among around 600 videos). Each video was rated 24 times. My purpose is to measure the inter-rater reliability for each group of videos (the videos that share a common concept), and later, the overall inter-rater reliability..
My proposition is to measure the Cronbach’s alpha coefficient for each video, and then to measure the average of those coefficients in order to asses the global Cronbach’s alpha coefficient related to one group of videos. I only need to know whether this approach is reliable, I mean computing the average of n Cronbach’s alpha coefficients (that were computed separately for each video) to get the inter-rater reliability for a group of videos makes a sense !
Thank you in advance for your help, I really appreciate it since I could not find an answer anywhere..
Best regards,
Ness
Ness,
I am not sure what you mean by measuring Cronbach’s alpha for one video. I would think that you would need more than one video even to use Cronbach’s alpha, unless you are comparing what you call “items”. In your explanation you reference 8 items, but I am not sure what the items represent.
My key question to you is why you want to use Cronbach’s alpha in this way, when, if I understand what you are trying to accomplish well enough, there are other tests which fit better with your goal? Perhaps you should be using Fleiss’s Kappa instead. See, for example, the webpage https://real-statistics.com/reliability/fleiss-kappa/.
Charles
Pls can someone send me how to solve cronbach alpha of the example1 above.thanks
Hi Charles,
Thanks for your prompt response and the info that you provided. I’ll download the software and give it a try. The 15-day trial version of the SPSS that I initially used kept outputing -4 as my alpha and it was frustrating.
Let me try again and if I encounter any problem, I’ll let you know.
Thanks again.
Ricky
Hello Charles,
I really need your help.
I am process of Writing my thesis and I need to find Cronbach’s alpha to state the reliability of my research. I tried usingg SPSS but I keep getting -4 as the alpha which I know is not right. It is a likert scale based questioonaire with a scale of 1 to 5 and the number of questions that I selected to find the Cronbach’s alpha is 10.
I will be glad to send you the questionnaire to see how you can help me.
regards, ricky
I would be willing to send you the data that I used.
I will be very grateful if you can assist me to solve this problem.
Ricky,
The referenced webpage explains how to calculate Cronbach’s alpha in Excel. If you have downloaded the Real Statistics software you can use the formula =CRONALPHA(R1) where R1 is the range containing your data (formatted as described on the webpage) and the software will do all the calculations for you.
Charles
Hi Charles,
I think I got it. Is it the sum of all the variance?
I got 1 different last digit than yours, instead of 3, I got 4.
I don’t know if it matters or not or if I am mistaken.
Thx again.
Arin,
Yes. It is the sum of the variances. I used the formula =SUM(B17:L17) which sums the values in each of the cells B17 through L17. Although the value displayed for each of these cells contains 5 digits, more than this number of digits are actually stored. If you simply add the numbers that are displayed you get a number which ends in 4. If instead you add the complete numbers (as the formula =SUM(B17:L17) does) then the result will end in 3.
Charles
Hi Charles,
Thanks so much for the explanation. It’s really easy to follow.
However, I have a question about example 1. How do you get the value for cell B20?
In figure 2, you just said its from M17. But how do you calculate it?
Any explanation on this would be very much appreciated.
Thx 🙂
Arin,
M17 contains the formula =SUM(B17:L17).
Charles
Thanks so much indeed Charles. I got it.
You have a Blessed day.
Best,
Hi Charles,
Thanks so much for this site. Very helpful.
Reading from one of your observations above, and I quote, “If the variances of the xj vary widely, the xj can be standardized to obtain a standard deviation of 1 prior to calculating Cronbach’s alpha”, end of quote. just wondering how do you do that. Would be grateful for your response.
Thanks
Hi Luke,
If you have a column of data in range A1:A10. You calculate the mean of the values (say in cell A12) by =AVERAGE(A1:A10) and the standard deviation (say in cell A13) by =STDEV(A1:A10). Now put the formula =STANDARDIZE(A1,A$12,A$13) in cell B1. B1 now contains the standardized value of the data in cell A1. If you highlight the range B1:B10 and press Ctrl-D then column B will contain the standardized values of all the data in range A1:A10.
Charles
Hye, i would like to run cronbach alpha on each item as my on likert scale..as you show in example 4 that run crunbach alpha on all the items..
How can i do it on each item?
Possible?
Seems it does not clear with me here..
Thanks
I’m not sure what you mean by “run cronbach on each item”. You run cronbach on all the items. You can also run cronbach on all the items except one (as in Example 2). In any case, how you calculate cronbach is described on the referenced webpage and you can get more information by looking at the example worksheet which you can download for free at webpage https://real-statistics.com/free-download/real-statistics-examples-workbook/.
Charles
hi. i gor high Cronbach for my 4 variables but the correlations are zero. Is it somehing wrong wih my calculations or the data? Need help. Tq
Dee,
Can you send me a file with the example so that I can take a look at it?
Charles
Thank you very much for this website!! Absolutely excellent and very useful…!
Hi there – hopefully you can answer me 🙂
I would like to run a Cronbachs alfa test (or similar if you have an alteriour suggestion) to include it in my reliability part. (using SPSS)
I have a mixture of variables – Nominal, Ordinal and scale.
Which have a whole range of diferent ranges in values. Some variables have 0-1, others have 1-5, while others go from 0-14000. None are similiarly kategorized. Like, sex is a 0-1. Work hours range pr week from 0-30. A satisfactory question ranges from 1-5, rent payed ranges from 500- 13000… etc..
I’ve kategorized rent, and when I lump them all togheter in SPSS – Cronbachs alfa I get a Cronbachs Alfa of around ,500.
BUT – I have a feeling this is quite pointless? Because of the state of the values – is this so, is Cronbachs Alfa usless – how would I explain that I can’t use Cronbachs Alfa? My corriculum states that it is restricted to indexes – But I can’t quite understand what this means by “indexes”. Certainly we have an index of questions that all aim to answer an underlying question – but it’s not an index where all numbers are grouped simillarilly – so i am unsure what it means… Can’t I use it ? 🙂
Colene,
I have read a lot of conflicting information regarding the subject you are raising and so I don’t have a precise answer for you. My understanding is that Cronbach’s alpha is most relevant when the test is evaluating a single “factor”. You can certainly calculate Cronbach’s alpha even if the questionnaire contains a mix of multiple choice, true-false and other types of questions. What I would be especially cautious about is when the test is performing different types of evaluations (e.g. Likert scale to assess your satisfaction with a product plus multiple choice to assess your ability to use the product). You definitely need to calculate separate Cronbach alpha for each concept/factor that you are testing.
I’m nor sure what your curriculum means by “indexes”. Cronbach’s alpha itself can be used as an index, but it doesn’t sound like this is what is meant.
The following are a couple of articles on the web that may give you further information (although they may confuse things even more). I suggest that you speak to your professor to get further insights from him/her. Please share with the rest of us any insights you glean.
http://www.ctbassessments.com/assessment_insights/february_2011/research_insights.html
http://psychweb.psy.umt.edu/denis/datadecision/front/cortina_alpha.pdf
Charles
Regarding example number 3, I have performed Anova: Two Factor without Replication in Excel, but could not see Alpha value as it has been shown in Figure 5 above.
Zargoon,
I just rechecked and I believe it is correct. Please make sure you analyzed the data from Example 1 (0’s and 1’s only) and not from Example 2.
Charles
You have to type the alpha value (and that line input) in yourself if using Excel….
Sorry, but I don’t know what you are referring to.
Charles
Hello,
I am having trouble with measures that has items with reverse coding. When I calculate the data with reverse coding, the Cronbach’s Alpha is very low (.2), however when I calculate the Cronbach’s Alpha without using the reverse coding, it is very high (.9). I am wondering if you know why that happens, and what I should do?
Dianna,
It is hard for me to tell without seeing the data, but I can think of the following possibilities:
– the questions that you have identified as reverse coded are not really reverse coded
– there is an error in the coding or calculation
– reliability is low (not sure why alpha would be high if reverse coding is not done)
Charles