Reliability and validity: Cronbach's alpha, examples, types

Learn how to calculate and interpret Cronbach's alpha, understand reliability and validity, and distinguish the types of validity. Includes a calculator and example.

A measuring instrument is reliable if it measures consistently, that is, if it keeps producing similar results with little random error. It is valid if it measures exactly what it's supposed to measure, and nothing else. Together with objectivity, reliability and validity are the three quality criteria of a questionnaire. Reliability is a necessary, but not a sufficient, condition for validity (Malhotra and Birks 2007, p. 359; Schumann 2019, pp. 30 and 42). Cronbach's alpha is the most widely used measure of one particular form of reliability: the internal consistency of a scale made up of several items (Schumann 2019, p. 42).

How to use the calculator. Use "Paste answers" to paste the answers to your scale items, or "Load file" to upload them: one column per item, one row per person. Mark the items that need to be reversed with "Reverse-code", usually the negatively worded ones. The calculator then shows Cronbach's alpha with a 95% confidence interval and, for each item, "Alpha if item deleted" and the "Corrected item-total correlation", that is, the item's correlation with the sum of the other items. To try it out, there's an example file with invented answers from 30 people to five items on job satisfaction. How to read the values is explained below under Cronbach's alpha.

In this article, you'll learn which errors distort a measurement, how to check reliability, how to calculate and interpret Cronbach's alpha, and which types of validity there are. How to build a scale is covered in Latent constructs and multi-item scales, and how to combine the items into one score in Aggregating multi-item (Likert) scales.

Measurement error: true score, random error and bias

Let's look at an example everyone knows: the bathroom scale. Imagine a scale that shows exactly 2 kilograms too much every time you weigh yourself. You step on it three times in a row and read the same number three times. So the scale measures consistently. It's reliable. But it doesn't show your weight, so it isn't valid (adapted from Schumann 2019, pp. 29-30).

Now a second scale. On average, it shows the right weight, but every time you step on it, the reading jumps up or down by a kilo or two. You can't trust this scale on any single reading. It has low reliability, and for that reason any single reading also has low validity.

And even the best bathroom scale isn't a valid instrument for measuring blood pressure (Schumann 2019, p. 30). Validity always refers to a particular purpose of measurement.

Another textbook offers a memorable image: a packet of cream of asparagus soup is reliable if it always tastes the same, and valid if it actually tastes of asparagus (Jacob et al. 2019, p. 39, n. 7).

The true score model

What happens with the bathroom scale is described by the true score model. The result of a measurement is not the true value of a characteristic but an observation of it (Malhotra and Birks 2007, p. 356; Marx 2026, slide 73). The observed score is made up of three parts:

Where:

X_O is the observed score, the value you see in your data set.

X_T is the true score of the characteristic.

X_S is systematic error. It affects every measurement in the same way, like the 2 kilograms of the first scale.

X_R is random error. It varies from one measurement to the next, like the jumps of the second scale.

Malhotra and Birks call the distinction between systematic and random error "crucial to our understanding of reliability and validity", because systematic error doesn't lower reliability, but random error does. If X_R is zero, the measurement is perfectly reliable (Malhotra and Birks 2007, p. 357). It's only perfectly valid if X_S is zero as well, in other words if there's no measurement error at all (Malhotra and Birks 2007, p. 358; Marx 2026, slide 74).

Errors come from sources such as socially desirable answers, fatigue, unclear wording or a poor layout (Malhotra and Birks 2007, p. 356). Much of this is in your own hands when you design the questionnaire.

Classical test theory has only one error term. There, reliability is the share of the variance of the true scores in the total variance (Fischer 1974, cited in Schumann 2019, pp. 30-31; Schnell 2019, p. 80, n. 32). Because true scores can't be determined empirically, reliability is estimated, not measured directly (Schumann 2019, p. 31).

Why reliability isn't enough

Three statements follow from the model, and they're worth remembering (Marx 2026, slide 75; Malhotra and Birks 2007, p. 359). A valid measurement is also reliable. A measurement with low reliability can't be highly valid. But reliability alone doesn't imply validity, because a perfectly reliable measurement can still contain systematic error.

So first you check reliability, then validity (Schumann 2019, p. 42). A high alpha doesn't yet prove that your scale measures the right thing. In my course, I quote Bart Gamble of Burke, Inc. on this: "The purpose of a scale is to enable us to represent respondents with the highest accuracy and reliability. We cannot have one without the other and still trust our data." (Marx 2026, slide 76).

Reliability: types and how to test it

Malhotra and Birks define reliability as "the extent to which a scale produces consistent results if repeated measurements are made" (Malhotra and Birks 2007, p. 357). That doesn't mean you always have to measure twice. There are four common methods for estimating it (Malhotra and Birks 2007, pp. 357-358; Schumann 2019, pp. 40-42):

Test-retest: asking twice

Malhotra and Birks give two to four weeks as the typical interval between the two measurements (Malhotra and Birks 2007, p. 357). For one scale described by Möhring and Schlütz, it was about two months (Beißert et al. 2015, cited in Möhring and Schlütz 2019, p. 19). The method assumes a stable characteristic and is therefore mostly used where several survey waves are planned anyway (Schumann 2019, p. 41). Online, I see it mainly in panels with the same people.

Parallel forms: two equivalent versions

Lienert and Raatz consider the parallel-forms method the best one when tested parallel versions are available (Lienert and Raatz 1998, cited in Schumann 2019, pp. 40-41). In surveys, that's practically never the case, so it's hardly used (Schumann 2019, p. 41). For the correlation, the same people have to answer both versions (Schumann 2019, pp. 40-41). The split-half method, by contrast, divides a single version into two groups of items.

Split-half: one survey, two halves

With the split-half method, you divide the items, for example into odd and even numbers, and correlate the sums of the two halves. The result depends on how you split (Malhotra and Birks 2007, p. 358). Because each half is only half as long, the correlation underestimates the reliability of the whole scale. The Spearman-Brown formula corrects for this if both halves have similar spread (Lienert and Raatz 1998, cited in Schumann 2019, p. 41, n. 60):

Schumann works with a correlation of 0.69 between the halves. Plugged in, that gives 2 · 0.69 / (1 + 0.69) = 1.38 / 1.69 ≈ 0.82 for the whole scale (Schumann 2019, p. 41, n. 60).

Internal consistency: the standard method

In practice, people mostly use methods that don't need a repeated measurement. Internal consistency is the most frequently used group of reliability tests and should be applied to all instruments made up of several indicators (Jacob et al. 2019, pp. 37-38). It assesses scales in which several items are added up to a total score (Malhotra and Birks 2007, p. 358). For an online survey with a single measurement, it's usually the method of choice. It just answers a different question than test-retest. Schnell explicitly warns against interpreting alpha as a measure of stability. A high alpha alone shows neither that the characteristic is stable over time nor that there's no measurement error. To assess stability, you need measurements at more than one time point (Schnell 2019, p. 80, n. 32).

And reliability isn't a fixed property of a scale. With a different sample, the coefficients can change. In the social sciences, there are no scales calibrated once and for all (Jacob et al. 2019, p. 39).

Cronbach's alpha: how to calculate and interpret it

Cronbach's alpha, also called coefficient alpha, can be understood as the average of all possible split-half coefficients of a scale (Cronbach 1951, cited in Malhotra and Birks 2007, p. 358). Today it's the most widely used coefficient of internal consistency (Schumann 2019, p. 42). This also tells you what alpha is not: not "the" measure of reliability, but a measure of one of its forms.

The formula

The formula needs only three ingredients (Utesch 2020, PDF p. 79):

Where:

k is the number of items in the scale.

Var(X_i) is the variance of the answers to item i. The sum runs over all k items.

Var(Y) is the variance of the total scores, that is, of each person's sum across all items.

The logic behind it: if the items measure the same thing, they go up and down together, and the variance of the total scores is much larger than the sum of the item variances. The fraction becomes small and alpha becomes large. If the items have nothing to do with each other, only their variances add up, and alpha is close to zero. The factor k / (k − 1) makes up for the fact that the fraction can't reach zero even if the items fit together perfectly.

Worked example: four items on job satisfaction

The data are invented. With eight people, this is a worked example, not a recommendation for a sample size.

An HR team measures job satisfaction with four statements. The response scale has five points with a neutral midpoint: 1 "strongly disagree", 2 "disagree", 3 "neither agree nor disagree", 4 "agree", 5 "strongly agree" (points adapted from Schumann 2019, p. 38).

• I1: "I enjoy going to work."
• I2: "My work is varied."
• I3: "All in all, I'm satisfied with my work."
• I4: "My work often frustrates me."

I4 is negatively worded. People who are satisfied disagree with it. Eight people answer like this:

Step 1: reverse-code. For negatively worded items, the values are reversed so that a high value means the same thing for every item (Schumann 2019, p. 38; Malhotra and Birks 2007, p. 349). On a scale from 1 to 5, you calculate 6 minus the value. A 2 becomes a 4, a 5 becomes a 1, and the midpoint 3 stays 3. How to combine the items into a scale score afterward is covered in Aggregating multi-item (Likert) scales.

Step 2: the item variances. Take I1. The mean is 3. The deviations from the mean are 2, 1, 1, 0, −1, 0, −1, −2. Squaring them gives 4, 1, 1, 0, 1, 0, 1, 4, which add up to 12. Divided by 8 − 1 = 7, that gives a variance of ≈ 1.714. I2 and I3 happen to have the same variance of ≈ 1.714, and the reversed I4 has 1.125. The sum of the item variances is ≈ 6.268.

Step 3: the variance of the total scores. The totals in the last column have a mean of 11.625. The sum of the squared deviations is 117.875, and divided by 7, that gives ≈ 16.839.

Step 4: plug in. With k = 4:

α = 4/3 · (1 − 6.268 / 16.839) ≈ 4/3 · (1 − 0.372) ≈ 0.84

So the four items fit together well. Whether you divide the variances by n or by n − 1 doesn't change alpha, as long as you do the same for all variances. The factor cancels out.

What happens if you forget to reverse-code

Let's calculate with I4 in its raw form. The item variances stay the same, because reversing doesn't change an item's spread, so their sum is again ≈ 6.268. The totals are now 15, 14, 15, 12, 12, 12, 11, 8. People who answer high on I1 to I3 answer low on I4, and the two partly cancel each other out in the total. The variance of the total scores drops to ≈ 5.411.

α = 4/3 · (1 − 6.268 / 5.411) ≈ 4/3 · (1 − 1.158) ≈ −0.21

Alpha is negative. That's not a calculation error but a warning sign: one item is running against the others. So when I see a strikingly low or negative alpha, the first thing I check is whether all negatively worded items have been reverse-coded.

Alpha if item deleted

Many statistics programs and the calculator above show, for each item, how high alpha would be if you left that item out. This isn't a separate method, just the same formula, once without I1, once without I2 and so on, each time with k = 3. For our example with I4 reversed:

Alpha with all four items: ≈ 0.84. My own calculation with the example data.

The right-hand column is the corrected item-total correlation, the correlation of an item with the total score of the other items. It's one of the criteria for deciding whether an item stays in the scale (Schumann 2019, pp. 39-40).

I2 is the item least related to the others. Without I2, alpha would rise from ≈ 0.84 to ≈ 0.90. So should the HR team drop I2? Not automatically. It's true that alpha can help you exclude items that aren't indicators of the construct (Jacob et al. 2019, p. 39). But whether variety is part of job satisfaction is a question of content. If you keep only items that ask almost the same thing, you'll get a nice alpha and may end up measuring only a slice of the construct. That's a question of content validity, more on that below.

Range: usually between 0 and 1

Textbooks give a range of 0 to 1 for alpha (Malhotra and Birks 2007, p. 358; Schumann 2019, p. 42; Jacob et al. 2019, p. 38). That holds as long as the items are, on average, positively related. If they're negatively related on average, as in the example with I4 not reversed, alpha becomes negative. Mathematically, it has no lower bound. A practitioner's book gives the range as minus infinity to 1 and says only positive values can be meaningfully interpreted (Weinreich and von Lindern 2008, pp. 166-167; likewise Marx 2020, slide 73).

What is a good Cronbach's alpha?

This is the question I'm asked most often.

0.7 is a common rule of thumb. The textbooks set the threshold differently: Malhotra and Birks at 0.6, German-language textbooks closer to 0.8 (Malhotra and Birks 2007, p. 358; Schumann 2019, p. 42; Jacob et al. 2019, p. 38; Döring and Bortz 2016, p. 468, cited in Möhring and Schlütz 2019, p. 102, n. 38).

My advice: below 0.6, I wouldn't trust a scale without looking for the cause. From about 0.8, internal consistency counts as sufficient according to all the sources above. In between, it depends on what you need the scores for. For an internal survey, 0.7 may be enough. For a publication, I'd be stricter. None of these values tells you whether the scale measures the right thing.

Alpha from a sample is an estimate. That's why the calculator also shows a 95% confidence interval using the method described by Feldt et al. (1987, p. 95). The method assumes a model with randomly sampled people and items, and independent, normally distributed error components with equal variance. With five-point answers, the interval should be read as an approximation. With small samples, interpret it with particular caution. For our example with eight people and four items, it runs from ≈ 0.52 to ≈ 0.96, for the example file with 30 people and five items from ≈ 0.66 to ≈ 0.90.

Three things that affect alpha

The number of items. Alpha tends to rise with the number of items (Peterson 1994 and Brown et al. 2002, cited in Malhotra and Birks 2007, p. 358). So only compare alpha values with the length of the scale in mind.

Redundant items. For the same reason, alpha can be "artificially, and inappropriately, inflated" when several items ask almost the same thing (Malhotra and Birks 2007, p. 358). You'll find examples in Latent constructs and multi-item scales. None of my sources gives a fixed upper limit. When I see values well above 0.9, I look at the wording and ask myself whether some items are just repetitions.

Several dimensions. If a scale measures a construct with several dimensions, internal consistency computed across all dimensions is inappropriate. Calculate alpha for each dimension instead (ibid.), for example one alpha for satisfaction with leadership and another for working conditions. The rule to remember: alpha assumes that the items measure the same thing. It doesn't prove it.

Types of validity at a glance

A scale is valid if differences in the observed scores reflect true differences between respondents and not errors (Malhotra and Birks 2007, p. 358). There's no single coefficient for this. Three types are usual, and it hardly makes sense to speak of "the" validity of a test (Schumann 2019, p. 42).

Content validity: is anything missing?

Content validity is "a subjective but systematic evaluation" of whether the items cover the whole domain of the construct (Malhotra and Birks 2007, p. 358). Schumann gives an example that fits our calculation well: a test of job satisfaction whose items refer only to income lacks content validity. Working atmosphere, supervisors, and opportunities for personal development and promotion are missing (Schumann 2019, p. 42).

Content validity is usually checked through expert judgment (Schumann 2019, p. 42). On its own, it isn't enough (Malhotra and Birks 2007, p. 358), but it's the counterweight to a purely numerical view.

Criterion validity: does the score match reality?

Criterion validity checks whether the scale is related to an external criterion. Malhotra and Birks give the example of a loyalty scale that is checked against observed repeat purchases (Malhotra and Birks 2007, pp. 358-359). Möhring and Schlütz mention statements about buying fair trade coffee that are compared with sales figures (Möhring and Schlütz 2019, p. 21).

Depending on when the criterion is measured, there are two forms (Malhotra and Birks 2007, p. 359; Schumann 2019, p. 43):

• Concurrent validity: the scale and the criterion are measured at the same time.
• Predictive validity: the criterion is measured later. The standard example is a school readiness test that has to prove itself against later school grades (Schumann 2019, p. 43).

For our HR example, that could mean: do teams with low job satisfaction have a higher voluntary turnover rate in the following year? To check this, compare the share of employees who resign in the same period, not the bare number of resignations. In an anonymous survey, this only works at the level of teams or departments, not for individuals. External criteria should preferably not be collected with further questions in the same questionnaire, but for example through observation or ratings by others. Otherwise, spurious relationships easily arise, for example because the same respondents tend to agree in both measurements (Schumann 2019, p. 43, n. 64).

One approach is the known-groups technique: groups known to have higher levels of a characteristic should score higher on the scale (Schumann 2019, p. 43). Möhring and Schlütz describe a media literacy scale that, as expected, showed higher scores for communication studies students than for school students (Sowka et al. 2015, cited in Möhring and Schlütz 2019, p. 102).

Construct validity: does the scale measure the intended property?

Construct validity asks which property a scale actually measures. It needs a theory, and Malhotra and Birks call it "the most sophisticated and difficult type of validity to establish" (Malhotra and Birks 2007, p. 359). It has three subtypes (ibid.):

• Convergent validity: the scale correlates highly with other measurements of the same construct.
• Discriminant validity: the scale can be distinguished empirically from measurements of other constructs. Different constructs may still correlate with each other.
• Nomological validity: the scale correlates with theoretically related constructs in the predicted ways.

Malhotra and Birks illustrate this with a scale on self-image. You'd expect high correlations with other self-concept scales (convergent), low correlations with brand loyalty and variety seeking (discriminant), and, as the theory predicts, respondents should prefer brands that match their self-image (nomological) (Malhotra and Birks 2007, p. 359).

A systematic method for this is the multitrait-multimethod matrix (Campbell and Fiske 1959, cited in Schumann 2019, p. 44). Construct validation is more a research program than a single test (Schumann 2019, p. 44).

By the way, "internal" and "external" validity are something else. External validity depends mainly on the sample (Möhring and Schlütz 2019, p. 20). That's the subject of the article Representative sample: what it is and how to check yours.

Example: is the NPS reliable and valid?

In my course, the Net Promoter Score appears in the chapter on reliability and validity, with two test questions (Marx 2020, slide 76): Is the scale reliable? Is the scale valid?

Reliable: the NPS is based on a single question. Cronbach's alpha can't be calculated for a single question, because the formula needs at least two items. That leaves test-retest, with the problems described above.

Valid: for what purpose? Reichheld himself later wrote with Markey that the recommendation question is the best single question for predicting customer behavior across a range of industries, but not in all of them, and that every company has to verify the link with later customer behavior empirically for its own business (Reichheld and Markey 2011, pp. 50-51, cited in Marx 2026, slide 78). In the language of this article, that's a call for predictive validity. What the research says about this and how to calculate the NPS is covered in the article Net Promoter Score (NPS): how to calculate and read it.

Objectivity: the third quality criterion of a questionnaire

A test should meet three main quality criteria: it should be objective, reliable and valid (Lienert and Raatz 1998, cited in Schumann 2019, p. 29). The same quality criteria apply to a questionnaire. There are three forms of objectivity (Schumann 2019, p. 29):

• Objectivity of administration: the result mustn't depend on who conducts the survey, for example which interviewer asks the questions.
• Objectivity of scoring: whoever analyzes the data must arrive at the same numerical result. Survey scoring is usually objective, although coding open-ended responses can involve judgment (Schumann 2019, p. 29).
• Objectivity of interpretation: different researchers mustn't draw different conclusions from the same score. Arbitrarily set cutoffs are a problem (Schumann 2019, p. 29).

Online, everyone sees the same text, and no interviewer influences the answers. But objectivity doesn't come automatically. Open answers need fixed coding rules. Before analyzing the data, decide what score you will use to classify a respondent as "satisfied". Möhring and Schlütz even consider objectivity unattainable and instead emphasize transparent methods that other researchers can follow and assess (Möhring and Schlütz 2019, p. 18).

What this means for your questionnaire

Adopt proven scales, with their source. In my course, the rule is "make or steal": for many constructs there are ready-made, tested scales, for example in the Marketing Scales Handbook (Bruner 2012, cited in Marx 2026, slide 69) or in academic journals. Keep the wording and the response options unchanged, and cite the source. But even proven scales have to be checked again in a new study, because context and respondents change (Schnell 2019, p. 123; Jacob et al. 2019, p. 39).

Use several items for constructs that can't be observed directly. Several items measure a characteristic more accurately than a single question (Malhotra and Birks 2007, p. 360).

Label every point. If only some points of a scale are labeled, or only numbers are given, the scale may be less clear and therefore less reliable and valid (Thielsch et al. 2012, p. 233). I also only use symmetric scales with a neutral midpoint. More on this in Likert scales: everything you ever wanted to know, but never dared to ask.

Use negatively worded items sparingly. Even when correctly reversed, they can lead to poor results in internal consistency tests, because many respondents struggle with double negatives (Möhring and Schlütz 2019, pp. 100-101). Note which items need reverse-coding right when you create the questionnaire.

Test before fieldwork. With a large enough pretest, you can already estimate reliability and validity (Schnell 2019, p. 123). For the item analysis of a new scale, Möhring and Schlütz recommend at least 100 people from the target group (Möhring and Schlütz 2019, p. 101). That applies to newly developed scales, not to every test run.

After fieldwork: calculate and report alpha for each dimension. Tests you've carried out, such as alpha coefficients, belong in the research report (Jacob et al. 2019, p. 248). Studies without information on the reliability and validity of their instruments are useless for scientific purposes (Schnell 2019, p. 126). For a thesis, that means: for each scale, state the number of items, the alpha value itself (not just "acceptable") and the source of the scale.

If alpha is low: check first, then drop. I first check whether all negatively worded items have been reverse-coded and whether the scale measures several dimensions. Then I look at the corrected item-total correlation and at alpha without the weakest item. I'd remove an item only if there were a substantive reason to do so, and I'd document that reason in the report.

By the way, among the QUESTIONSTAR templates you'll also find established instruments with their source, for example the template Employee wellbeing & stress (PSS-10 + WHO-5) with the WHO-5 and the Perceived Stress Scale. But even an established scale needs to be checked with your own data.

How to calculate it with your own data

QUESTIONSTAR itself doesn't calculate Cronbach's alpha. With the answers from your survey, you have three options.

With the calculator above. Export your answers as an XLSX or CSV file and copy the item columns into the calculator at the top of this article.

With a statistics program. For SPSS, R or the free JASP, export the data as an SPSS, CSV or XLSX file. The common statistics programs offer standard procedures for split-half and alpha (Jacob et al. 2019, p. 38, n. 6). Besides alpha, they usually also show the corrected item-total correlation and alpha if item deleted.

With an AI assistant. If QUESTIONSTAR is connected to an AI assistant via the MCP interface, for example in ChatGPT or Claude, the assistant can calculate Cronbach's alpha from your survey's answers. The assistant does the calculation, not QUESTIONSTAR. Tell it which items belong to the scale and which need reverse-coding. Questions you've marked as personal data in the survey aren't passed to the assistant when that setting is switched on. Answers without this marking, especially free text, can still contain personal data. So check before the transfer which questions the assistant will get to see. And check the result, for example with the calculator above or in a statistics program.

Whichever way you choose, keep three things in mind:

1. Reverse-code negatively worded items before the analysis, or you'll calculate with the wrong sign, as in the example.
2. Calculate alpha separately for each dimension, not for the whole questionnaire.
3. Check how missing answers are coded in the export. Such codes mustn't enter the calculation as scale values.

QUESTIONSTAR itself calculates correlations, regressions and t-tests, in reports and via the MCP interface. For individual questions, that's a first look: how strongly are two items related? Do two groups differ on a question, for example teams you expect to differ? Keep the limitation from above in mind: a criterion from the same survey is only a weaker test. For the scale score and for alpha, use one of the three options above. How the t-test works is explained in the article The t-test: comparing means the methodologically clean way.

Frequently asked questions about reliability and validity

What is the difference between reliability and validity?

Reliability asks whether an instrument produces consistent results with little random error (Malhotra and Birks 2007, p. 357). Validity asks whether it measures what it's supposed to measure (Schumann 2019, p. 30).

Can a test be reliable but not valid?

Yes. A systematic error that affects every measurement in the same way doesn't lower reliability, but it makes the measurement invalid. Conversely, a measurement with low reliability can't be highly valid (Malhotra and Birks 2007, p. 359).

What types of validity are there?

Three types are usual: content validity, criterion validity with its concurrent and predictive forms, and construct validity with its convergent, discriminant and nomological subtypes (Malhotra and Birks 2007, pp. 358-359; Schumann 2019, pp. 42-43).

What is a good Cronbach's alpha?

There's no single threshold. Malhotra and Birks consider 0.6 or less unsatisfactory (Malhotra and Birks 2007, p. 358), while German-language textbooks call values above 0.8 acceptable or good (Schumann 2019, p. 42; Jacob et al. 2019, p. 38). The common rule of thumb of 0.7 lies in between.

Can Cronbach's alpha be too high?

A very high value can point to items that ask almost the same thing, because redundant items inflate alpha artificially (Malhotra and Birks 2007, p. 358). My sources give no fixed upper limit. With values well above 0.9, it's worth taking a look at the wording.

What is objectivity?

Objectivity, reliability and validity are the three main quality criteria (Lienert and Raatz 1998, cited in Schumann 2019, p. 29). A survey is objective if the results don't depend on who conducts, analyzes and interprets it (Schumann 2019, p. 29).

How do I calculate Cronbach's alpha?

You divide the sum of the item variances by the variance of the total scores, subtract the result from 1 and multiply by k / (k − 1), where k is the number of items. Reverse-code negatively worded items first. In practice, you calculate it with the calculator above, or with SPSS, R or JASP.

Sources

Beißert, H., Köhler, M., Rempel, M. and Beierlein, C. (2015). Deutschsprachige Kurzskala zur Messung des Konstrukts Need for Cognition NFC-K [German short scale for measuring the construct need for cognition, NFC-K]. Zusammenstellung sozialwissenschaftlicher Items und Skalen (ZIS). In German. Cited in Möhring and Schlütz (2019), p. 19.

Brown, T. J., Mowen, J. C., Donavan, D. T. and Licata, J. W. (2002). The customer orientation of service workers: personality trait effects on self- and supervisor performance ratings. Journal of Marketing Research, 39(1), 110-119. Cited in Malhotra and Birks (2007), p. 358.

Bruner (2012). Marketing Scales Handbook, Vol. 6. Cited in Marx (2026), slide 69.

Campbell, D. T. and Fiske, D. W. (1959). Convergent and Discriminant Validation by the Multitrait-Multimethod-Matrix. Psychological Bulletin, 81-105. Cited in Schumann (2019), p. 44.

Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. Cited in Malhotra and Birks (2007), p. 358.

Döring, N. and Bortz, J. (2016). Forschungsmethoden und Evaluation in den Sozial- und Humanwissenschaften [Research methods and evaluation in the social and human sciences] (5th ed.). Berlin: Springer. In German. Cited in Möhring and Schlütz (2019), p. 102, n. 38.

Feldt, L. S., Woodruff, D. J. and Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11(1), 93-103. Online.

Fischer, G. (1974). Einführung in die Theorie psychologischer Tests [Introduction to the theory of psychological tests]. Bern. In German. Cited in Schumann (2019), pp. 30-31.

Jacob, R., Heinz, A. and Décieux, J. P. (2019). Umfrage. Einführung in die Methoden der Umfrageforschung [Surveys: an introduction to survey research methods] (4th ed.). Berlin/Boston: De Gruyter Oldenbourg. In German.

Lienert, G. A. and Raatz, U. (1998). Testaufbau und Testanalyse [Test construction and test analysis] (6th ed.). Weinheim. In German. Cited in Schumann (2019), pp. 29, 40-41 and 41 n. 60.

Malhotra, N. K. and Birks, D. F. (2007). Marketing Research. An Applied Approach (3rd European ed.). Harlow: Pearson Education.

Marx, P. (2020). Grundlagen der Umfrageforschung [Principles of survey research] (slide deck, 2020 version). Slide 73 (reliability and validity) and slide 76 (NPS in the chapter on reliability and validity). In German.

Marx, P. (2026). Principles of Survey Research. Online course, Chapter 2 "Survey: Measurement and Scaling", slides 69, 73-76 and 78. QUESTIONSTAR. Course, chapter 2.

Möhring, W. and Schlütz, D. (2019). Die Befragung in der Medien- und Kommunikationswissenschaft. Eine praxisorientierte Einführung [Surveys in media and communication studies: a practical introduction] (3rd ed.). Wiesbaden: Springer VS. In German.

Peterson, R. A. (1994). A meta-analysis of Cronbach's coefficient alpha. Journal of Consumer Research, 21, 381-391. Cited in Malhotra and Birks (2007), p. 358.

Reichheld, F. and Markey, R. (2011). The Ultimate Question 2.0. Boston: Harvard Business Review Press. pp. 50-51, cited in Marx (2026), slide 78.

Schnell, R. (2019). Survey-Interviews. Methoden standardisierter Befragungen [Survey interviews: methods of standardized questioning] (2nd ed.). Wiesbaden: Springer VS. In German. DOI 10.1007/978-3-531-19901-6.

Schumann, S. (2019). Repräsentative Umfrage. Praxisorientierte Einführung in empirische Methoden und statistische Analyseverfahren [Representative surveys: a practical introduction to empirical methods and statistical analysis] (7th ed.). Berlin/Boston: De Gruyter Oldenbourg. In German.

Sowka, A., Klimmt, C., Hefner, D., Mergel, F. and Possler, D. (2015). Die Messung von Medienkompetenz. Ein Testverfahren für die Dimension "Medienkritikfähigkeit" und die Zielgruppe "Jugendliche" [Measuring media literacy: a test for the dimension "critical media skills" and the target group "adolescents"]. Medien & Kommunikationswissenschaft, 63(1), 62-82. In German. Cited in Möhring and Schlütz (2019), p. 102.

Thielsch, M. T., Lenzner, T. and Melles, T. (2012). Wie gestalte ich gute Items und Interviewfragen? [How do I design good items and interview questions?] In M. T. Thielsch and T. Brandenburg (eds.), Praxis der Wirtschaftspsychologie. Bd. II, Themen und Fallbeispiele für Studium und Anwendung [Business psychology in practice, vol. II: topics and case studies for study and application] (pp. 221-240). Münster: Monsenstein und Vannerdat. In German.

Utesch, T. (2020). Workshop slide deck on quality criteria, reliability and factor analysis (untitled). University of Münster (Westfälische Wilhelms-Universität Münster), December 15 to 17, 2020. Unpublished. In German. Page numbers refer to the PDF version.

Weinreich, U. and von Lindern, E. (2008). Praxisbuch Kundenbefragungen [Customer surveys: a practical handbook]. München: mi-Fachverlag, FinanzBuch Verlag. In German.

I wish you scales you can trust, and the courage to report a middling alpha openly.

Related articles:

• Latent constructs and multi-item scales
• Aggregating multi-item (Likert) scales
• Net Promoter Score (NPS): how to calculate and read it

Dr. Paul Marx

Author: Dr. Paul Marx
Dr. Paul Marx is the founder and Managing Director of QUESTIONSTAR and was a professor of marketing at the University of Siegen.