{"id":363131,"date":"2026-08-02T06:40:09","date_gmt":"2026-08-02T06:40:09","guid":{"rendered":"https:\/\/peraltafinancing.com\/analytics\/understanding-alpha-inflation-measuringu\/"},"modified":"2026-08-02T06:40:09","modified_gmt":"2026-08-02T06:40:09","slug":"understanding-alpha-inflation-measuringu","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=363131","title":{"rendered":"Understanding Alpha Inflation \u2013 MeasuringU"},"content":{"rendered":"


\n<\/p>\n

\n

\"Feature<\/a>The large sample size. The right statistical tests. A compelling and statistically significant finding! All the ingredients of a successful quantitative project that gets stakeholder buy-in. But inflation isn\u2019t just a worry for the Federal Reserve on interest rate policy. It affects research decisions, too.<\/p>\n

When you conduct something like a usage and attitude survey with hundreds or thousands of participants (like what we do with our industry reports<\/a>), you have the benefit of statistical power (the ability to detect differences). This allows you to look not only for differences between main effects (like between software products), but also for interactions (differences by type of user by product).<\/p>\n

With enough power, you can dig into these more nuanced differences. For example, you may learn that younger adults have different usage patterns and attitudes than older cohorts for certain products. It would be a compelling story, and it\u2019s something that stakeholders can make sense of and act on. We\u2019ve seen it and reported it. But how do you know these differences aren\u2019t a fluke?<\/p>\n

You may think limiting yourself to reporting only statistically significant findings will protect you from these false positives, and that approach certainly helps. But like printing money to boost the economy, the more statistical tests you run, the more you inflate your chances of finding things that aren\u2019t actually there.<\/p>\n

This isn\u2019t monetary policy; it\u2019s alpha inflation. It\u2019s a subtle concept that you should understand when making multiple statistical comparisons.<\/p>\n

Alpha (False Alarm Rate) in Hypothesis Testing<\/span><\/h2>\n

In null hypothesis significance testing<\/a> (NHST), the alpha criterion is the value selected for decisions of statistical significance. This is the process through which you decide if a difference is statistically significant. As shown in Figure 1, when the p<\/em>-value you get from a statistical test is less than the alpha value you set, you reject the hypothesis of no difference (the null hypothesis, H0<\/sub>). It\u2019s statistical significance! Otherwise, you fail to reject H0<\/sub> (you don\u2019t accept it; you just don\u2019t have enough evidence to reject it).<\/p>\n

\"Figure<\/a><\/p>\n

Figure 1:<\/strong> High-level flowchart of statistical hypothesis testing.<\/p>\n

The whole point of this process is to control the percentage of false alarms (rejecting H0<\/sub> when there really is no difference) in the long run<\/strong>. We\u2019ve previously discussed why the alpha criterion doesn\u2019t have to be the standard p<\/em> , but the rationale for using .05 was published by R. A. Fisher in 1929: \u201cIt is a common practice to judge a result significant, if it is of such a magnitude that it would have been produced by chance not more frequently than once in twenty trials [.05]. This is an arbitrary, but convenient, level of significance for the practical investigator.\u201d<\/a><\/p>\n

So, when you run one test of significance, if there is really no difference, you have a 5% chance of mistakenly concluding that there is a difference. That\u2019s fine if you\u2019ve collected data from two groups (A and B), but what if you\u2019ve collected data from three groups (A, B, and C) and want to compare A with B, B with C, and A with C? Or, as in the case of the usage and attitude survey, you want to make dozens of comparisons of subgroups (such as age or usage levels across product versions)?<\/p>\n

For all these scenarios, you\u2019ll have to deal with the consequences of alpha inflation.<\/p>\n

What Is Alpha Inflation?<\/span><\/h2>\n

When we declare a difference as statistically significant when p<\/em> Type I errors in statistical jargon, will happen and are expected.<\/p>\n

At the p<\/em> UX-Lite\u00ae<\/sup> scores of two products). But what if you run more than one statistical test? Software makes it very easy to run all sorts of comparisons such as the differences between age cohorts, experience levels, and products. What if you run 5, 10, 20, or 100 tests? You\u2019re printing money and, like the inflation rate, your false alarm rate goes up too.<\/p>\n

To understand how running more tests increases your false alarm (Type I) error rate, Table 1 shows the probability of zero false alarms, one false alarm, two false alarms, and so forth.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
x (Number of false alarms)<\/th>\np<\/i>(x) when \u03b1\u00a0=\u00a0.05<\/i><\/i><\/th>\np<\/i>(at least x) when \u03b1 = .05<\/i><\/i><\/th>\n<\/tr>\n<\/thead>\n
0<\/td>\n0.36<\/td>\n1.00<\/td>\n<\/tr>\n
1<\/td>\n0.38<\/td>\n0.64<\/td>\n<\/tr>\n
2<\/td>\n0.19<\/td>\n0.26<\/td>\n<\/tr>\n
3<\/td>\n0.06<\/td>\n0.08<\/td>\n<\/tr>\n
4<\/td>\n0.01<\/td>\n0.02<\/td>\n<\/tr>\n
5<\/td>\n0.002<\/td>\n0.003<\/td>\n<\/tr>\n
6<\/td>\n0.0003<\/td>\n0.0003<\/td>\n<\/tr>\n
7<\/td>\n0.00003<\/td>\n0.00003<\/td>\n<\/tr>\n
8\u201320<\/td>\n0.00000<\/td>\n0.00000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

<\/p>\n

Table 1:<\/strong> Alpha inflation for 20 tests conducted with \u03b1<\/em> = .05.<\/p>\n

As shown in Table 1, the most likely number of Type I errors in a set of 20 independent tests with \u03b1<\/em> = 0.05 is one, with a point probability of 0.38. That is, when you run 20 comparisons, there\u2019s a 38% chance of getting one false alarm<\/strong>. The next highest point probability is 0.36 for 0 false alarms, meaning you have about the same chance of having no false alarms in a set of 20 comparisons as you do one false alarm.<\/p>\n

Unfortunately, you can encounter more than one false alarm in a set of 20 tests. The likelihood of at least one Type I error, however, is higher (specifically, 1 \u2212 p<\/em>(0) = 1 \u2212 0.36 = 0.64). That\u2019s a 64% chance of 1, 2, 3, or more. (Although more than two or three false alarms in 20 comparisons is rare.) So, rather than having a 5% chance of encountering a Type I error when there is no real difference, \u03b1<\/em> has inflated to 64%.<\/p>\n

What Can You Do About Alpha Inflation?<\/span><\/h2>\n

You can\u2019t raise interest rates to tame alpha inflation. But since the middle of the 20th century, many strategies and techniques have been published to guide the analysis of multiple comparisons, such as omnibus tests (e.g., ANOVA<\/a> and MANOVA<\/a>) and procedures for the comparison of pairs of means (e.g., Tukey\u2019s WSD<\/a> and HSD<\/a> procedures, the Student\u2013Newman\u2013Keuls test<\/a>, Dunnett\u2019s test<\/a>, the Duncan procedure<\/a>, the Scheff\u00e9 procedure<\/a>, the Bonferroni adjustment<\/a>, and the Benjamini\u2013Hochberg adjustment<\/a>).<\/p>\n

With all these methods available to handle alpha inflation, the problem is solved\u2014right?<\/p>\n

Controlling Alpha Inflation Has Its Consequences<\/span><\/h2>\n

When the null hypothesis is not true, applying techniques to control alpha inflation (decreasing the number of Type I errors) necessarily increases the number of Type II errors\u2014the failure to detect differences that are real. An overemphasis on the prevention of Type I errors leads to the proliferation of Type II errors.<\/p>\n

Unless, for your situation, the cost of a Type I error is much greater than the cost of a Type II error, you should avoid applying any of the techniques designed to suppress alpha inflation. As Perneger (1998<\/a>, p. 1236) wrote, \u201cSimply describing what tests of significance have been performed, and why, is generally the best way of dealing with multiple comparisons.\u201d In UX and many applied research settings, failing to detect a real difference can be just as harmful as falsely declaring a difference. Context matters, so don\u2019t think Type I errors should take all the focus.<\/p>\n

Or, as Abelson (1995<\/a>, p. 70) put it, \u201cRandom patterns will seem to contain something systematic when scrutinized in many particular ways. If you look at enough boulders, there is bound to be one that looks like a sculpted human face. Knowing this, if you apply extremely strict criteria for what is to be recognized as an intentionally carved face, you might miss the whole show on Easter Island.\u201d<\/p>\n

We pay more attention to alpha inflation when we\u2019re making many unplanned comparisons. But even then, we have a balanced approach to managing Type I and Type II errors, which we\u2019ll cover in an upcoming article.<\/p>\n

Summary and Discussion<\/span><\/h2>\n

Alpha inflation is what happens when running multiple statistical tests quietly erodes the reliability of your p<\/em>\n<\/p>\n

Alpha inflation is real. <\/strong>Run 20 independent comparisons at \u03b1<\/em> = .05, and you don\u2019t have a 5% chance of a false alarm anymore; you have a 64% chance of at least<\/em> one. The reality of alpha inflation can easily be demonstrated using binomial probabilities (as in Table 1).<\/p>\n

Many methods have been developed to control alpha inflation. <\/strong>The methods, primarily developed in the 20th century, vary considerably in their relative conservatism (judging fewer contrasts to be significant) and liberalism (judging more contrasts to be significant).<\/p>\n

But you can\u2019t just raise interest rates to fix alpha inflation. <\/strong>Controlling alpha inflation has hidden costs. Controlling only Type I errors (false alarms) leads to a proliferation of Type II errors (misses). The decision to use methods to control alpha inflation depends strongly on the relative costs of Type I and Type II errors in a specific research context. We\u2019ll cover how to strike that balance in an upcoming article.<\/p>\n<\/p><\/div>\n\n","protected":false},"excerpt":{"rendered":"

The large sample size. The right statistical tests. A compelling and statistically significant finding! All the ingredients of a successful quantitative project that gets stakeholder buy-in. But inflation isn\u2019t just a worry for the Federal Reserve on interest rate policy. It affects research decisions, too. 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