{"id":246,"date":"2026-09-07T09:19:47","date_gmt":"2026-09-07T07:19:47","guid":{"rendered":"https:\/\/iq-test.org\/blog\/?p=246"},"modified":"2026-09-07T09:19:49","modified_gmt":"2026-09-07T07:19:49","slug":"iq-test-reliability","status":"publish","type":"post","link":"https:\/\/iq-test.org\/blog\/en\/iq-test-reliability\/","title":{"rendered":"43,651 Tests Analyzed: How Reliable Is the IQ Test?"},"content":{"rendered":"\n

In short:<\/strong> I analyzed 43,651 historical test sessions from IQ-Test.org. The result is strong: Taken together, the 46 questions included in the analysis show remarkably consistent performance. Cronbach’s alpha and McDonald’s omega are both approximately 0.88. Most individual questions are also meaningfully related to the overall score, and the response patterns reveal a clear common performance factor.<\/p>\n\n\n\n

However, this internal analysis does not show whether the reported IQ score would exactly match the result of a professionally administered intelligence test. It first examines how reliably the test works as a measurement instrument in its own right. Reliability, validity and other requirements for a sound test are related, but they are not the same thing. [1]<\/p>\n\n\n\n

Online IQ tests often use words such as \u201cscientific,\u201d \u201caccurate\u201d and \u201creliable.\u201d These claims are only useful when it is clear what was actually examined.<\/p>\n\n\n\n

I have been running IQ-Test.org for more than ten years. During that time, the site has accumulated a large body of test data, allowing me to examine the test much more closely today than when it was first launched. I focused on four questions:<\/p>\n\n\n\n

    \n
  1. How consistently do the questions work together as one test?<\/li>\n\n\n\n
  2. How easy or difficult are the individual questions?<\/li>\n\n\n\n
  3. How well do they distinguish between lower and higher overall performance?<\/li>\n\n\n\n
  4. What common structure can be found in the response patterns?<\/li>\n<\/ol>\n\n\n\n

    The main part of this article explains the results in accessible language. Readers who want to examine the calculations more closely will find a detailed methodology section and the scientific sources at the end.<\/p>\n\n\n\n

    Key results at a glance<\/h2>\n\n\n\n
    Measure<\/th>Result<\/th>What it means<\/th><\/tr>
    Test sessions analyzed<\/td>43,651<\/td>The analysis included historical cases that passed internal checks and were marked as suitable for norming.<\/td><\/tr>
    Questions analyzed<\/td>46<\/td>These questions had been scored consistently throughout the period covered by the analysis.<\/td><\/tr>
    Cronbach’s alpha<\/td>0.876<\/td>The questions show high internal consistency.<\/td><\/tr>
    McDonald’s omega<\/td>0.875<\/td>A different statistical model produces virtually the same result.<\/td><\/tr>
    Questions with corrected item-total correlation \u2265 0.30<\/td>32 of 46<\/td>Around 70% of the questions are clearly related to performance on the rest of the test.<\/td><\/tr>
    First factor<\/td>Eigenvalue 12.98<\/td>The response patterns reveal a dominant common performance factor.<\/td><\/tr>
    Loadings on the first factor \u2265 0.30<\/td>39 of 46<\/td>Most questions make a recognizable contribution to this common factor.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    What data did I analyze?<\/h2>\n\n\n\n

    I included 43,651 historical test sessions that had passed an internal plausibility check and were marked norm_valid = 1<\/code>, meaning they were considered suitable for use in the norming dataset. For this analysis, I examined only the answers to the test questions. Age, gender and other demographic characteristics were not included.<\/p>\n\n\n\n

    Each question was scored as either correct or incorrect. Every completed test therefore produced a sequence of zeros and ones: 1 for a correct answer and 0 for an incorrect answer. The total score used in this analysis was the number of correct answers across the 46 usable questions.<\/p>\n\n\n\n

    On average, participants answered 24.45 of the 46 questions correctly. The median was 25, and the standard deviation was 8.00 points. The scores therefore varied enough to examine differences between participants and how the individual questions performed.<\/p>\n\n\n\n

    Why I analyzed 46 rather than 47 questions<\/h3>\n\n\n\n

    When I reviewed the historical data, I found a problem with question 40 (q40): For a period of time, the incorrect answer key 115<\/code> had been stored for this question. The database records only whether an answer was considered correct or incorrect according to the key in use at the time. The participants‘ original answers are no longer available.<\/p>\n\n\n\n

    That means the historical data cannot be genuinely corrected after the fact. I therefore excluded q40 from the total score, reliability calculations, item-total correlations and factor analysis. All 43,651 test sessions could still be retained in the sample.<\/p>\n\n\n\n

    Question 40 has since been corrected in the live test. Once enough new responses have been collected and scored consistently, I will be able to analyze it again.<\/p>\n\n\n\n

    How reliably do the questions work together?<\/h2>\n\n\n\n

    In this article, \u201creliability\u201d primarily refers to the internal consistency<\/strong> of the overall scale: Do people who solve many questions also tend to perform well on other questions in the same test?<\/p>\n\n\n\n

    An internally consistent test contains questions that contribute meaningfully to a shared overall result rather than behaving as unrelated or contradictory tasks. The questions do not have to be identical. What matters is that they work together in a coherent way.<\/p>\n\n\n\n

    Cronbach’s alpha: 0.876<\/h3>\n\n\n\n

    Cronbach’s alpha is a widely used measure of internal consistency. Put simply, it considers how strongly the questions are related to one another in relation to the variation in total test scores. The coefficient was introduced by Cronbach in 1951. [2]<\/p>\n\n\n\n

    For the 46 questions analyzed here, alpha is 0.876<\/strong>. This is clear evidence of high internal consistency for the overall scale.<\/p>\n\n\n\n

    On its own, however, alpha does not prove that the test measures only one ability or that the reported IQ score is correctly calibrated against an external standard. It is also influenced by the number of questions in the test. I therefore interpret alpha together with omega, the corrected item-total correlations and the factor analysis. [4]<\/p>\n\n\n\n

    McDonald’s omega: 0.875<\/h3>\n\n\n\n

    McDonald’s omega addresses a similar question but is based on a factor model. Unlike alpha, this model can account for the fact that individual questions may be related to the common measurement target to different degrees. [6]<\/p>\n\n\n\n

    At 0.875<\/strong>, omega is almost identical to alpha. Two measures built on different assumptions therefore lead to the same conclusion: The total score across the 46 questions has high internal consistency.<\/p>\n\n\n\n

    How difficult are the individual questions?<\/h2>\n\n\n\n

    For questions scored as correct or incorrect, item difficulty<\/strong> is straightforward: It is the proportion of participants who answered a question correctly.<\/p>\n\n\n\n

    If 80% of participants solve a question, its value is 0.80\u2014or 80%. Under this definition, a higher percentage means an easier question in this sample.<\/p>\n\n\n\n

    \"Percentage
    Figure 1: Percentage of correct answers for each usable question. Based on my analysis of 43,651 test sessions. Some information has been obscured to protect the test; further details are available on request.<\/em><\/figcaption><\/figure>\n\n\n\n

    The proportion of correct answers ranges from 98.13% for q2<\/strong> to 2.19% for q46<\/strong>. The median across all questions is 53.76%<\/strong>, placing the typical question near the middle of the observed difficulty range.<\/p>\n\n\n\n

    Overall, 37 of the 46 questions were answered correctly by between 20% and 80% of participants. Four questions were solved by more than 90%, while two were solved by no more than 10%.<\/p>\n\n\n\n

    This wide range of difficulty is a strength of the test. Easier opening questions make the test more accessible and help capture performance at the lower end of the range. More demanding questions can provide better differentiation at the upper end.<\/p>\n\n\n\n

    Together, this mix allows the test to measure participants across a broad range of performance. The questions are not concentrated at a single difficulty level. Whether a particular question actually distinguishes well between lower and higher performers is examined through its item-total correlation.<\/p>\n\n\n\n

    Which questions distinguish most clearly between participants?<\/h2>\n\n\n\n

    A question can have an appropriate level of difficulty and still contribute little to the overall test. I therefore also calculated its corrected item-total correlation<\/strong>, commonly used as a measure of item discrimination.<\/p>\n\n\n\n

    This value shows whether people who answer a particular question correctly also tend to score higher on the other 45 questions. \u201cCorrected\u201d means that the question being examined is removed from the comparison score, so it cannot artificially increase its own correlation. [8]<\/p>\n\n\n\n

    \"Corrected
    Figure 2: Corrected item-total correlation for each question. The line at 0.30 is a rough reference point, not a fixed quality threshold. Based on my analysis. Some information has been obscured to protect the test; further details are available on request.<\/em><\/figcaption><\/figure>\n\n\n\n

    For 32 of the 46 questions, the corrected item-total correlation is at least 0.30. The median is 0.362<\/strong>, and q38 has the highest value at 0.562<\/strong>.<\/p>\n\n\n\n

    This means that around 70% of the questions meet the reference value of 0.30 used here. I treat values below 0.20 as a reason for closer review. These are not rigid cutoffs: Very easy or very difficult questions can have lower correlations because there is less variation in the responses, yet they may still serve a useful purpose in the test.<\/p>\n\n\n\n

    Question 35 (q35) stands out with a value of just 0.017<\/strong>. Whether a participant solved this question was therefore almost unrelated to their performance on the rest of the test. Question 11 (q11) is also comparatively weak at 0.067<\/strong>.<\/p>\n\n\n\n

    Low values can have several causes, including unclear presentation, more than one plausible solution, an unsuitable answer key or a response pattern that differs substantially from the rest of the test. I will therefore review q35 and q11 and then decide whether to retain, revise or replace them.<\/p>\n\n\n\n

    The overall test does not depend on any single question. Removing q35 would raise alpha only slightly, from 0.876 to 0.879<\/strong>. The finding is therefore mainly a specific opportunity to improve the question pool.<\/p>\n\n\n\n

    Do the questions measure a common factor?<\/h2>\n\n\n\n

    Reliability alone does not show whether the responses share an underlying structure. To examine this, I conducted an exploratory factor analysis.<\/p>\n\n\n\n

    Factor analysis looks for patterns: Which questions tend to be solved by the same people, and can these relationships be described by one or more common performance factors? A factor is not a directly observed trait. It is a statistical summary of shared response patterns.<\/p>\n\n\n\n

    Because each answer is recorded only as correct or incorrect, I based the factor analysis on tetrachoric correlations. This approach assumes that an underlying continuous ability or tendency to solve the problem gives rise to the observed binary response. Tetrachoric correlations are commonly used when conducting factor analyses of binary or ordinal items. [9]<\/p>\n\n\n\n

    \"Eigenvalues
    Figure 3: Eigenvalues of the tetrachoric correlation matrix. The clear gap between the first and subsequent factors indicates a dominant common factor. Based on my analysis.<\/em><\/figcaption><\/figure>\n\n\n\n

    The first eigenvalue is 12.98<\/strong>, while the second is 2.45<\/strong>. The first is therefore approximately 5.3 times as large as the second. This indicates a common performance factor with a particularly strong influence on the response patterns. The first factor accounts for 28.2% of the total variance in the tetrachoric correlation matrix. This is not a measure of test reliability and does not indicate how reliable the test is overall.<\/p>\n\n\n\n

    In the one-factor solution, 39 of the 46 questions have a loading of at least 0.30. Participants who perform well in one part of the test therefore also tend to perform better on other questions. This provides a reasonable foundation for calculating one overall score.<\/p>\n\n\n\n

    Not every question follows exactly the same response pattern, so the analysis does not indicate a perfectly unidimensional test. I did not investigate separate ability domains in this analysis.<\/p>\n\n\n\n

    Several eigenvalues are greater than 1, but I do not interpret this automatically as evidence of several distinct abilities. The simple rule of retaining every factor with an eigenvalue above 1 can produce too many small factors when a test contains many items. [10]<\/p>\n\n\n\n

    Overall, the data support a dominant common performance factor and therefore support the use of a total score. They do not, by themselves, prove that this score is an exact measure of general intelligence.<\/p>\n\n\n\n

    What I am taking from the analysis<\/h2>\n\n\n\n

    For me, the analysis provides more than a set of summary statistics. It also identifies specific ways to improve the test:<\/p>\n\n\n\n