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Tag: statistics

  • A Roadmap for Choosing a Statistical Test: From Research Question to the Right Tool in 5 Questions

    The question I receive most often from students and early-career researchers is not “how do I run this test in SPSS?” but “which test should I use?” And the answer is almost always: “it depends.” Depends on what? On a few things that can actually be answered with five simple questions.

    If you answer these five questions honestly before opening any software, you will avoid picking an unsuitable test, and the defense room becomes a much friendlier place.

    Question 1: What is the goal of the analysis?

    There are four main goals, and each points to a different family of tests:

    • Comparing (is there a difference between groups or over time?)
    • Relating (are two variables associated?)
    • Predicting or explaining (which variables influence another variable?)
    • Grouping or summarizing (is there a hidden structure in the data?)

    Write your goal in one ordinary sentence before choosing a test. “I want to know whether average satisfaction differs between new and long-standing customers.” That sentence already shows the direction: a comparison of two groups.

    Question 2: What is the measurement scale of your variables?

    The measurement scale determines which mathematical operations make sense.

    • Nominal: categories without order (gender, city, brand).
    • Ordinal: ordered categories (education level, satisfaction ranking).
    • Interval/ratio: numbers with meaningful distances (income, age, test score, body weight).

    Likert variables are often treated specially. A single Likert item is strictly ordinal, while a combined score from many items is often treated as interval. That practice is common, but it should be stated and justified.

    Question 3: How many groups are compared, and are they independent or paired?

    Two questions in one. How many groups? Two, or more than two. Independent or paired? Independent means the groups consist of different subjects (for example men and women). Paired or repeated means the same subjects are measured more than once (for example scores before and after training) or matched pairs.

    Question 4: Are the assumptions of parametric tests met?

    Parametric tests (for example the t-test and ANOVA) assume certain things, such as a roughly normal distribution and comparable variances across groups. If those assumptions are clearly violated (for example a small sample with very skewed data, or ordinal data), a non-parametric alternative that does not rely on distributional assumptions is usually safer. But remember: non-parametric tests also have assumptions and are generally less powerful when the parametric assumptions are actually met.

    Question 5: What is the size and nature of your sample?

    A very small sample limits the choice of tests and makes assumption checks unreliable. A clustered sample (for example students within classes) violates the independence assumption and calls for special approaches (for example multilevel models).

    Quick selection tables

    Here is the short guide I use as a starting point. It does not replace judgment, but it saves time.

    Comparing groups on a numeric/ordinal variable

    SituationIf parametric assumptions are metNon-parametric alternative
    Two independent groupsIndependent samples t-testMann-Whitney test
    Two paired groupsPaired t-testWilcoxon test
    Three or more independent groupsOne-way ANOVAKruskal-Wallis test
    Three or more measurements on the same subjectsRepeated-measures ANOVAFriedman test

    Categorical variables

    SituationTest
    Relationship between two categorical variables (independent groups)Chi-square test (or Fisher’s test if expected frequencies are small)
    Dichotomous change in the same subjects (before-after)McNemar’s test
    Three or more dichotomous measurements on the same subjectsCochran’s Q test

    Relating variables

    SituationMeasure
    Two numeric variables, linear relationshipPearson correlation
    Ordinal data or assumptions not metSpearman or Kendall correlation
    Two categorical variablesPhi, Cramer’s V

    Predicting or explaining

    SituationTechnique
    One numeric dependent variable, one predictorSimple linear regression
    One numeric dependent variable, many predictorsMultiple linear regression
    Binary dependent variable (yes/no)Logistic regression
    Many relationships at once among latent variablesSEM or PLS-SEM
    Direct and indirect effects among observed variablesPath analysis

    Three good habits when choosing a test

    1. Decide on the test before seeing the results. Choosing a test after seeing which one gives a significant result is a recipe for false findings. Write your analysis plan at the start.

    2. Always report effect sizes and confidence intervals, not just p-values. Every test has a suitable effect size: Cohen’s d for a difference between two means, eta squared for ANOVA, regression coefficients for regression, and so on.

    3. Check assumptions on the right object. Normality in a t-test is checked within each group, and in regression on the residuals, not on the pooled raw variable.

    One complete example

    A training manager wants to know whether a new training program improves employees’ competence scores. She measures the same score on 40 employees before and after the training.

    • Goal: compare two measurements.
    • Scale: competence score (interval).
    • Groups: one group, two measurements, paired.
    • Assumptions: what is checked is the normality of the difference between the after and before scores.
    • Choice: paired t-test (if the differences are roughly normal) or Wilcoxon test (if not).
    • Reporting: the mean difference, its confidence interval, the effect size, and a practical explanation.

    The same five questions guide almost every test choice, from the simplest to the most complex. Mastering the logic is far more valuable than memorizing software menus.

    Three more examples to build intuition

    Example 1. A researcher wants to know whether education level (high school, bachelor’s, master’s) is related to the choice of digital payment method (three types of e-wallet). Both variables are categorical, with independent groups. The choice: Chi-square test, with Cramer’s V as a measure of association to show the strength of the relationship.

    Example 2. A team wants to compare task completion time across four interface designs, each tried by different people. Numeric variable, four independent groups. If the residuals are roughly normal and variances comparable: one-way ANOVA with a post hoc test. If the data is highly skewed and the sample small: Kruskal-Wallis.

    Example 3. A manager wants to predict whether a customer will cancel a subscription (yes or no) from subscription length, number of complaints, and usage frequency. Binary dependent variable, mixed predictors. The choice: logistic regression, evaluated with measures such as recall, precision, and AUC.

    A short assumptions checklist

    Before trusting the result of a t-test or ANOVA, check: independence of observations, normality (within groups or of residuals), and homogeneity of variance (for example Levene’s test). For regression: linearity, independence of errors, homoscedasticity, normality of residuals, and absence of severe multicollinearity. If an assumption is clearly violated, do not stop there: consider a transformation, a test that is more robust to violations, or a more suitable model.

    Short Q&A

    What if I am comparing two groups but the sample sizes are very unbalanced? A t-test with a correction for unequal variances (Welch’s test) is usually safer than the standard t-test. Also note that a very small group limits precision, whatever the test.

    Is it acceptable to run many tests on the same data? Yes, as long as you report all of them and account for multiple testing. The more tests you run, the greater the chance of finding a ‘significant’ result by chance, so the significance threshold needs to be adjusted or the results interpreted more carefully.

    Unsure which statistical test fits your research? The datalytics.indo team can help with everything from formulating the research question and designing the analysis, through carrying it out (regression, CB-SEM and PLS-SEM, path analysis, difference tests, non-parametric tests, factor analysis, clustering, and more), to interpretation. Private tutoring in SPSS and in-house applied statistics training are also available. Let’s discuss your needs first. We’ll provide a tailored quote based on your project.

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  • Ice Cream and Drowning: Why Correlation Is Not Causation (and How to Test It Properly)

    In statistics lectures, there is one classic example that never gets boring. Researchers collect monthly data and find that when ice cream sales rise, the number of drowning cases rises too. The correlation is strong. The chart is pretty, two lines moving up and down together like two dancers who have rehearsed.

    The question: should we ban ice cream at the beach?

    Of course not. And you have probably guessed why. Hot weather makes people buy more ice cream, and hot weather also makes more people swim. More people swimming means more people drowning. Ice cream and drowning both rise because of a third cause. Statisticians call it a confounder.

    The example is funny, but the same mistake happens every day in the real world: in company reports, in the news, and, most often, in theses. Let us take it apart so you do not get fooled.

    What exactly is correlation?

    Correlation measures how strongly two variables move together. Its value (the correlation coefficient) ranges between −1 and +1. Close to +1 means both tend to rise together, close to −1 means one rises when the other falls, and around 0 means there is no clear linear pattern.

    The method depends on the measurement scale of the variables. For two numeric variables with a linear relationship, we use Pearson correlation. For ranked data or data that does not meet the assumptions, we use Spearman or Kendall. For two categorical variables (for example gender and product choice), we use measures of association such as Phi or Cramer’s V. These tools are useful, but they all answer the same question: “do the two move together?” Not: “does one cause the other?”

    Four reasons two things can correlate without causing each other

    1. A confounder (a third cause). Like ice cream and drowning. Another example: people who carry matches in their pockets are more likely to get lung cancer. It is not the matches that cause it, but the smoking habit that makes them carry matches.

    2. Reversed direction of cause and effect. We suppose A causes B, when B actually causes A. For example, you find that employees who attend training more often perform better. Maybe training improves performance, but maybe managers more often send already high-performing employees to training.

    3. Coincidence. If you search enough pairs of variables, some pairs will appear correlated by chance alone. There are websites that collect silly correlations, such as per capita cheese consumption tracking the number of people who died by becoming tangled in their bedsheets. The correlation is high, the meaning is zero. The more hypotheses you test, the greater the chance of finding a false relationship.

    4. A deceptive pattern because data is combined (Simpson’s paradox). A trend visible in the combined data can reverse when the data is split into groups. For example, a hospital looks worse than another overall, but when viewed by patient severity, it is actually better at every level. The reason: that hospital receives more patients in serious condition. Combining data without thinking about its composition hides the truth.

    So how can we claim cause and effect?

    Establishing cause and effect is harder than computing a correlation, and it demands design, not just formulas. There are several approaches, from the strongest:

    • Randomized controlled experiments. Researchers randomly assign subjects to treatment and control groups. Because assignment is random, known and unknown confounders tend to be balanced between groups. This is the gold standard, but it is not always possible or ethical.
    • Natural experiments and quasi-experimental designs. When we cannot randomize, we look for natural situations that resemble randomization, or compare changes before and after a policy between affected and unaffected groups (for example a difference-in-differences design).
    • Statistical control. We include known confounders in a regression model to “remove” their influence. This is useful, but only as good as the list of confounders you know and measure. Unobserved confounders remain dangerous.
    • Theoretical reasoning and layered evidence. In fields that are hard to experiment in (for example epidemiology), cause-and-effect conclusions are built from many studies, plausible mechanisms, a clear time order, and consistency of findings.

    For a thesis with a one-time survey, the practical message is this: use language proportionate to your design. Write “is related to” or “is associated with”, not “causes” or “has an impact on”, unless your design truly supports it. And state plainly that you cannot rule out other explanations.

    An example from the workplace

    Suppose the HR department finds that employees who joined a mentoring program have a lower turnover rate. The tempting conclusion: “Mentoring lowers turnover, let’s extend it to all employees.” But before deciding, ask:

    • Who joined mentoring? If more motivated employees are more likely to sign up, the difference may reflect motivation, not the effect of mentoring.
    • Are there other differences between participants and non-participants (division, tenure, salary)?
    • Can we test it through a limited pilot with random selection?

    Those questions may seem to slow things down, but they actually save money. Expanding a program whose effect is illusory costs far more than running a careful small pilot.

    A quick way to detect misleading claims

    Whenever you hear a claim that “A causes B”, ask these five questions:

    1. Could B be causing A?
    2. Is there a third thing causing both?
    3. Could the relationship arise purely by chance (how many other relationships were tried)?
    4. Is there a fair comparison, meaning a group that is similar except for A?
    5. Is there a plausible mechanism explaining how A affects B?

    If the claim fails three of the five questions, treat it as a hypothesis, not a fact.

    Ice cream does not make people drown. But the habit of drawing conclusions from two lines that move together has “drowned” a lot of business decisions and research.

    How to report a correlation properly

    A well-reported correlation includes five things: the coefficient (for example r = 0.42), the number of observations, the confidence interval, the p-value as a supplement, and a scatterplot. The scatterplot matters because the same number can come from very different patterns. There is a classic example called Anscombe’s quartet: four datasets with nearly identical means, variances, and correlations, but with completely different shapes, some a straight line, some curved, some driven by a single outlier. Without looking at the chart, we can conclude the wrong thing.

    To interpret the strength of a relationship, a commonly used guideline (which is rough and depends on the field) calls an absolute value of about 0.10 weak, 0.30 moderate, and 0.50 and above strong. But in the social sciences, a correlation of 0.30 is often already considered meaningful. So the context of the field needs to be considered.

    Need help testing relationships between variables in your data with the right method and interpreting them honestly? The datalytics.indo team can help with everything from research design, through analysis (correlation, regression, CB-SEM and PLS-SEM, path analysis, factor analysis, clustering, and more), to interpretation. Private tutoring and in-house training are also available. Let’s discuss your needs first. We’ll provide a tailored quote based on your project.

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  • What Does a P-Value Actually Say? 6 Misconceptions Still Taught in Many Classrooms

    If there is one number that is most often worshipped and most often misunderstood in research, it is the p-value. Students memorize it: “if p is less than 0.05, the hypothesis is accepted; if more, it is rejected.” Lecturers ask about it at the defense. Journals use it as a yardstick. And in the middle of all that, almost nobody can truly explain what the number means.

    I am not blaming anyone. The definition really is not intuitive. But understanding it correctly can save you from wrong conclusions, in a thesis and in the workplace. Let us start with the definition, then take apart the six most common misconceptions.

    The correct definition, in human language

    The p-value is the probability of getting a result as extreme as the one we observed (or more extreme), assuming the null hypothesis is true. The null hypothesis usually says “there is no effect” or “there is no difference”.

    Imagine you suspect a coin is unfair. You flip it ten times and get nine heads. The question: if this coin were actually fair, how likely would we be to get a result this extreme? The probability of getting nine or ten heads out of ten flips of a fair coin is about 1.1%. That is the p-value (for a one-sided test): about 0.011. A small number means your result is surprising if the coin is fair, so you begin to doubt the assumption that the coin is fair.

    Notice what it does not say: the p-value does not tell you the probability that the coin is fair. It only tells you how odd the data is if the coin is fair. Two very different things, and that is the root of the misconceptions that follow.

    Misconception 1: “p = 0.03 means the null hypothesis has a 3% chance of being true”

    Wrong. The p-value is the probability of the data (or more extreme) assuming the null hypothesis is true, not the probability that the null hypothesis is true given the data. Flipping that sentence is like equating “the probability that someone carries an umbrella if it is raining” with “the probability that it is raining if someone carries an umbrella”. The two are clearly different. To get the probability of the hypothesis itself, we need a different approach (for example Bayesian) and prior information about how plausible the hypothesis was before seeing the data.

    Misconception 2: “p < 0.05 means the effect is important”

    No. The p-value does not measure the size of an effect. With a very large sample, a trivial difference (for example a satisfaction score difference of 0.02 on a scale of 1 to 5) can produce a very small p. Conversely, with a small sample, a practically important effect can produce a large p because the data is not strong enough to establish it.

    To judge the importance of an effect, report the effect size (for example a difference in means, a regression coefficient, Cohen’s d, or R²) along with a confidence interval. A confidence interval is far more informative: it shows the range of plausible effect values, not just yes or no.

    Misconception 3: “p > 0.05 means there is no effect”

    Also wrong. A non-significant result only means the data is not strong enough to reject the null hypothesis. Perhaps the effect truly does not exist. Perhaps the effect exists, but the sample is too small to detect it (low power). “No evidence of an effect” is not the same as “evidence of no effect”. In a report, write “insufficient evidence was found” and show the confidence interval to make clear whether a meaningful effect is still possible.

    Misconception 4: “0.05 is a sacred number”

    The 0.05 threshold is a convention, not a law of nature. It became popular in the early 20th century because it was easy to use with statistical tables, not because there is any scientific reason that 0.049 is fundamentally different from 0.051. Treating p = 0.049 as a “finding” and p = 0.051 as “not a finding” is a fragile way of thinking. In its 2016 statement, the American Statistical Association warned that scientific conclusions and policy decisions should not be based only on whether a p-value passes a specific threshold.

    Misconception 5: “If I try many analyses and one is significant, that is my finding”

    This is a subtle trap, and often unnoticed by those who fall into it. If you test 20 relationships that do not actually exist, with a 0.05 threshold, you should expect about one “significant” result by chance. The probability that at least one of 20 independent tests produces p < 0.05 when there is no effect at all is about 64%. If you report only the significant one, you are presenting coincidence as discovery.

    The practice of trying various analyses, picking subgroups, or deleting data until a significant result appears is called p-hacking. How to guard against it: set your hypotheses and analysis plan before looking at the data, report all the analyses you ran (not just the ones that worked), and use corrections for multiple testing when testing many hypotheses at once.

    Misconception 6: “A very small p-value means the result is certainly true”

    A small p-value does not guarantee that the study design is good, the measurement valid, the sample representative, or that there is no bias. A perfect analysis of flawed data still produces flawed conclusions. The p-value answers only one narrow question about random variation, and does not touch questions about data quality or research logic.

    So how should you use the p-value?

    The view I share with students and researchers:

    1. Understand what is being tested. Write the null hypothesis in plain words.
    2. Report the actual p-value (for example p = 0.031), not just “p < 0.05”.
    3. Always include the effect size and confidence interval.
    4. Consider power. Is your sample sufficient to detect a meaningful effect?
    5. Tell the whole story of your analysis. Do not hide analyses that did not work.
    6. Combine it with theory and common sense. A significant result that contradicts all existing theory deserves suspicion and replication.

    The p-value is not the enemy. It is a useful tool, as long as it is used to answer the right question. What is dangerous is turning it into a traffic light that decides “true or false” without thinking.

    A numerical example: the same effect, different conclusions

    Imagine a training program raises the average competence score by 2 points on a scale with a standard deviation of 10 (a small effect, Cohen’s d = 0.2). If we test it on 30 people, that effect will almost certainly not be detected (large p), and we might conclude ‘the training has no effect’. If we test it on 3,000 people, the same effect will produce a very small p, and we conclude ‘the training has a significant effect’. The effect is exactly the same: two points. Only the sample size changed. The question that really matters is: is two points meaningful in practice, and is the cost of the training proportionate to the benefit? The p-value does not answer that.

    Alternatives and complements

    Several increasingly recommended approaches: confidence intervals to show the range of plausible effects, effect sizes to state magnitude, power analysis before a study to make sure the sample is sufficient, pre-registration of analysis plans to prevent choosing analyses after seeing results, and replication to check whether findings hold up. Bayesian approaches also offer a way to state how strongly the evidence supports a hypothesis, though they require additional understanding. The point is not to throw away the p-value, but to place it as one piece of evidence among several.

    Processing data for a thesis, dissertation, or journal manuscript and want your interpretation to hold up in front of examiners and reviewers? The datalytics.indo team can help with everything from research design and sampling, through analysis (regression, CB-SEM and PLS-SEM, path analysis, factor analysis, clustering, and more), to interpretation and writing up results. Private tutoring in SPSS and SmartPLS is also available. Let’s discuss your needs first. We’ll provide a tailored quote based on your project.

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  • 5 Data Analysis Mistakes That Most Often Get Theses and Dissertations Marked Down at the Defense

    I will not pretend that the thesis defense room is friendly. A good examiner’s job is to keep asking until you cannot answer. The good news is that the questions that make students nervous almost always come from the same list. After years of working with students, lecturers, and researchers, and having taught at several universities before that, I have seen the same mistakes appear again and again, semester after semester.

    Here are the five data analysis mistakes I run into most often, along with how to fix them before the examiner finds them first.

    Mistake 1: Testing normality on the wrong object

    This is number one because almost everyone has done it. Students run a normality test (Kolmogorov-Smirnov or Shapiro-Wilk) on every variable, then conclude “the data is not normal, so I must use a non-parametric test.” But for linear regression, the normality assumption applies to the model’s residuals, not to the raw variables. And for a two-group comparison, what you check is the distribution within each group, not all the data pooled together.

    Two more notes: with large samples, formal normality tests can reject normality because of trivial deviations. With small samples, the tests are too weak to detect problems. So do not rely on the p-value alone. Look at histograms and Q-Q plots too, and consider the central limit theorem. For Likert scales, many researchers treat the combined score as interval data. That is common practice, but it should be explained and defended, not quietly done.

    Mistake 2: Not being able to justify your sample

    “My sample is 100 people because I calculated it with the Slovin formula.” Then the examiner asks: “From what population? How did you choose them? Do they represent the population?” And the answer: “I sent the questionnaire to my friends…”

    A sample size without a clear selection method only satisfies a numerical requirement, not a scientific one. If your sample is not random, do not disguise it. Say honestly that it is purposive or convenience sampling, explain why, and state its limitations: your results must not be generalized to the whole population with confidence. Examiners respect honesty about limitations far more than a fragile claim of generalization.

    Mistake 3: Misunderstanding validity and reliability

    There are two versions of this mistake.

    Version one: skipping instrument testing entirely, or simply taking a questionnaire from another study without retesting it on your sample.

    Version two: assuming a high Cronbach’s alpha means the instrument is valid. Alpha measures internal consistency (reliability), not validity. An instrument can be very consistent and still measure the wrong thing. Like a rice scale that always shows the same number very consistently, but is not suitable for weighing gold. Reliable, but not valid for your purpose.

    For construct validity, use factor analysis (exploratory or confirmatory) or, in PLS-SEM, outer loadings, AVE, and discriminant validity. For reliability, report Cronbach’s alpha or composite reliability, and explain the interpretation. And remember, alpha tends to rise as the number of items increases, so a high value on a long instrument is not always impressive.

    Mistake 4: Chasing “significant” and forgetting to ask “how big”

    Many results and discussion chapters turn into a list of p-values: “significant”, “not significant”, “significant”, “significant”. No effect sizes, no confidence intervals, and no substantive explanation.

    A p-value answers only one narrow question: how surprising is this data if there were actually no effect? It does not say how large or how important the effect is. With a large sample, a very small effect can be “significant”. With a small sample, a meaningful effect can be “not significant”. Also report coefficients, effect sizes (for example R², Cohen’s d, or path coefficients with their intervals), and explain their practical meaning in language a layperson can understand.

    A related temptation: trying various analyses, removing “troublesome” respondents, or constantly changing the model until the result is significant. In the literature this practice is called p-hacking, and an experienced examiner can smell it. Decide the analysis based on theory before seeing the results, and record every change you make along with the reasons.

    Mistake 5: Conclusions that go beyond the data

    This last mistake is subtle. Your study is a one-time survey of 150 students at one campus, and the conclusion reads: “Leadership causes performance improvement among all employees in Indonesia.”

    There are two leaps there. The first leap: from correlation to cause and effect. One-time survey data can only show a relationship, not direction and cause. The word “causes” requires a stronger design. The second leap: from sample to population. A sample from one campus does not automatically represent the whole country.

    Use language proportionate to the strength of your data: “is associated with”, “is related to”, “supports the idea that”, and state the limits of generalization openly. The limitations section of a study is not a sign of weakness, but a sign of scientific maturity.

    A note on integrity

    In every engagement, I always emphasize one principle: the purpose of helping with analysis is not to let students “just receive the finished result”, but to make sure they understand what they are doing and can defend it in front of examiners. An answer you do not understand is a trap waiting in the defense room. That is why good tutoring always comes with explanation, not just a finished result.

    Quick checklist

    Before submitting your results chapter, ask yourself:

    1. Have I run my assumption tests on the right object?
    2. Can I explain how the sample was selected and where its generalization ends?
    3. Have I reported validity and reliability with the correct interpretation?
    4. Have I reported effect sizes and a substantive explanation, not just p-values?
    5. Is my conclusion proportionate to the strength of the data and the research design?

    If all five answers are “yes”, you are already better prepared than most people at a defense.

    Examples of improved sentences in the results chapter

    A few sentences I often come across, and healthier versions:

    • Before: ‘The data is not normal, so a non-parametric test was used.’ After: ‘The model residuals met the normality assumption based on a Q-Q plot and the Shapiro-Wilk test, so linear regression was used.’
    • Before: ‘The sample is 100 according to the Slovin formula.’ After: ‘The sample of 100 respondents was selected purposively from employees of the marketing division. Results are not generalized to the whole company.’
    • Before: ‘The instrument is valid and reliable because alpha is 0.91.’ After: ‘The instrument has good internal consistency (alpha 0.91), and construct validity is supported by factor analysis with loadings above 0.60.’
    • Before: ‘Leadership has a significant effect (p < 0.05).’ After: ‘Leadership is positively associated with performance (coefficient 0.34; 95% confidence interval 0.18 to 0.50), with a medium effect size.’

    The differences look small, but to an examiner, the sentences in the second version show that you understand what you did.

    Short Q&A

    Is it acceptable to use a parametric test even if the data is not normal? In many cases, yes, especially with sufficiently large samples because of the central limit theorem, or when the chosen test is robust to mild violations. What matters is that you check the assumptions properly, consider alternatives, and explain your choice.

    What if my supervisor suggests something different? Discuss it with data and methodological reasons, not defensively. Often the difference comes from conventions in a particular field. Explaining your choice clearly shows that you understand, and that works in your favor at the defense.

    Working on your results and discussion chapter, or stuck on data analysis? The datalytics.indo team can help with everything from research design, instrument testing, and analysis (regression, CB-SEM and PLS-SEM, path analysis, factor analysis, clustering, and more), through to interpretation, with explanations that help you understand the results. Private tutoring in SPSS, SmartPLS, and LISREL/AMOS is also available. Let’s discuss your needs first. We’ll provide a tailored quote based on your project.

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  • An Average Salary of IDR 54.5 Million? Hold On: 4 Questions to Ask Before You Believe a Number

    Imagine you are job hunting. A job ad says, in bold letters: “Average employee salary: IDR 54.5 million per month!” Your heart skips, your CV is sent off, and you are already picturing your mortgage getting paid off early.

    Then on your first day at the office you learn the small print. The company has ten people. Nine of them earn IDR 5 million. The tenth, who happens to be the owner, pays himself IDR 500 million.

    Do the math yourself: (9 × 5 million + 500 million) ÷ 10 = 54.5 million. The ad did not lie. The number is correct. But do you feel deceived? Of course you do.

    This is exactly why I have stayed in statistics for so long, and why it also frustrates me. Statistics almost never lies. What lies is the way we present and read it. The keynote I once gave at a university took its title from this idea: How to Lie with Statistics. Not to teach people to lie, but so that they are not easily lied to.

    After more than twenty years working with surveys, political research, academic studies, and dashboards for oil and gas and automotive companies, I have found a repeating pattern. Almost every misleading number gets through because people forget to ask four simple questions. Let us go through them one by one, slowly, without formulas that give you a headache.

    1. An average of what, and who was left out?

    Back to that office. Besides the average (the mean), there is another measure called the median: the middle value when all the data is lined up from smallest to largest. In that office the median salary is IDR 5 million. And IDR 5 million is what most employees actually experience.

    Why is the gap so large? Because the mean is like an overly sensitive scale: a single extreme value is enough to push it. Imagine weighing rice on a gold scale. The reading may be accurate down to the milligram, but the instrument does not suit what you need. For skewed data, such as income, house prices, or savings balances, the median is almost always more honest.

    A practical rule: if the mean and the median are far apart, an extreme value is “pulling” the number. Do not stop at one number. Look at the spread too.

    The second question matters just as much: who is not being counted? Take a customer satisfaction survey filled in only by active customers. The result will almost certainly look good, because disappointed customers have already left and are not on the respondent list. Experts call this survivorship bias: we only see those who stayed, and assume everything is fine. If you judge a company by the employees who remain, you may miss the stories of those who resigned.

    2. How many people were surveyed, and how were they chosen?

    “The survey involved 10,000 respondents!” Sounds convincing. But the more important question is where those 10,000 people came from.

    If a survey link is shared in one chat group full of like-minded people, ten thousand responses are really just one voice repeated ten thousand times. Conversely, 400 people chosen at random from a clearly defined population can give a far more trustworthy picture.

    On margin of error, here is an easy rule of thumb for a survey with a 95% confidence level:

    • A sample of 300 people: margin of error of about ±5.7%
    • A sample of 400 people: about ±4.9%
    • A sample of 1,000 people: about ±3.1%

    So if a random survey says 52% of respondents choose A and 48% choose B with a sample of 400, that four-point gap is still swallowed by the margin of error. A headline saying “A leads” becomes too bold. This is why surveys and quick counts demand discipline: sample size, sampling method, and margin of error must be stated openly. If all three are missing, treat the number as an opinion wearing a statistics costume.

    3. Compared with what?

    A number without a comparison is like a 3-0 score with no idea who the opponent was: it sounds great, but nobody knows what it means. “Our sales grew 20%.” Good, until you learn that the whole market grew 35% in the same period. Compared with the market, you actually fell behind.

    A fair comparison has three conditions: per capita (so large regions do not automatically win or lose), the same period (do not compare Eid season with an ordinary month), and the same definition (the one most often forgotten).

    A telling example is in crime data. Big cities almost always lead in the number of crime cases, but that is because they have many residents. Once you divide by population, the ranking can flip.

    Business dashboards work the same way. I once helped build a 21-page dashboard to monitor six regions at an oil and gas company. No dashboard, however beautiful, is useful if the numbers on each page have no clear comparison: against target, against last month, or against another region. A director does not need many charts. A director needs charts that answer the question “are we doing well or badly?”.

    4. Who made this chart, and what do they want to show?

    The fourth question is about staying alert. Charts are a very powerful tool of persuasion, which also makes them the easiest to abuse. Some tricks that appear often:

    • A truncated axis. The vertical axis does not start at zero, so a small difference looks like a big jump.
    • Mismatched scales. Two charts side by side with different scales give an impression of similarity that is not real.
    • A hand-picked period. A trend looks like a sharp rise only because the chart starts exactly at the lowest point.
    • Percentages without the base number. “Up 300%” can mean going from 1 case to 4 cases.

    That does not mean every chart maker intends to deceive. Often it is simple carelessness. But as readers, we do not need to know the intent. We only need to check the axis, the scale, the period, and the base figure before we believe.

    One small habit that changes how you read numbers

    The four questions boil down to one habit: do not accept a number as fact; treat it as a claim to be tested. A good claim has nothing to fear from testing. A shaky claim looks shaky the moment you ask, “of what, from whom, compared with what, and who made it?”

    This habit helps everywhere: reading the news, reading an office report, judging an investment offer, even writing a thesis. Students who get used to asking this usually level up quickly when writing their results and discussion chapters, because they stop reporting numbers and start interpreting them.

    And if one day the data in front of you feels too complicated, or its conclusion feels off, that is not a sign you are not smart enough. It is a healthy signal that something needs to be checked again.

    Writing a thesis or dissertation, or need your institution’s data read honestly? I and the team at datalytics.indo help from research design and instrument testing, through analysis (regression, CB-SEM and PLS-SEM, path analysis, factor analysis, clustering, and more), to interpretation of results. Private tutoring in SPSS, SmartPLS, LISREL, Power BI, and Excel/VBA is also available. Let’s discuss your needs first. We’ll provide a tailored quote based on your project.

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