This happens when the results of a study or test don’t reflect the true situation. It’s the difference between the actual value and the one you measure or estimate. Statistical error may occur as the result of samples that don’t appropriately reflect the population, or incomplete data rather than observing entire populations or absolute truths.
What Is A Null Hypothesis? (often written as H₀)
This is the starting assumption in any test, or the “default position.” It usually states that there’s no effect or no difference between groups (e.g., a new drug doesn’t work better than a placebo, or a new campaign experiment is not better than the original). In statistical analysis, the goal of a test is to either reject or fail to reject this assumption based on data.
In simplest terms, one might treat the Null Hypothesis as a normal behavior, meaning “there is no causal link between the variables we’re analyzing.” When analyzing the results of a test, you then either reject or fail to reject the null hypothesis.
Reject the Null Hypothesis: This means the evidence (data) suggests that the null hypothesis is unlikely to be true. It’s like saying, “Based on the data, we believe the new drug does have an effect.” Or, “We have enough evidence to doubt the default assumption of no impact, the experiment campaign is better than the control campaign.” However, remember that rejecting a null hypothesis does not mean better or worse – it means the variables being tested do have a causality between them that is not statistical error.
Fail to Reject the Null Hypothesis: This means the data doesn’t provide enough evidence to conclude that the null hypothesis is wrong. It’s like saying, “We don’t have enough proof to claim the drug works better than nothing” or “we don’t have conclusive data to suggest a campaign experiment is having an impact.” However, this doesn’t mean the null hypothesis (the default position of no effect) is true, just that you don’t have strong enough evidence to dismiss it.
Why “fail to reject” – simply because it’s not proof, and conditions (including how testing is done) can also change the outcome. In the example below, we wouldn’t say that the fire alarm not going off when there’s no fire is proof that the fire alarm works perfectly (the test condition isn’t considering this), nor would we say that there’s an absolute guarantee that a fire alarm not going off is proof there’s no fire – because conditions might change. This is a different standard from Rejecting the Null Hypothesis = our default condition isn’t explained by the variable we’re testing, so the variable caused some measurable difference.
False Negatives & False Positives
There’s two ways you could misinterpret data, leading to incorrectly rejecting or failing to reject the null hypothesis. Again, rejecting the null hypothesis means “the results of the test on these variables indicates it’s more than just natural happenstance.” Likewise failing to reject the null hypothesis means there was not evidence sufficient to state the variables being tested influence the outcome, but it does not mean there’s a definitive finding.
Both rejecting and failing to reject the null hypothesis can have errors. In short: Type 1 errors are false alarms, and Type 2 errors are missed signals.
What Is A Type 1 Error?
This occurs when you reject the null hypothesis when it’s actually true.
In other words, it’s a “false positive” – you think you’ve found an effect or difference when there really isn’t one.
This is like sounding an alarm when there’s no fire, declaring a placebo cures a condition, or identifying a campaign experiment has a positive impact on performance when it had no effect.
What Is A Type 2 Error?
This occurs when you fail to reject the null hypothesis even though it’s false.
It’s a “false negative” – you fail to observe a real effect or difference.
This is like a fire alarm not triggering when there is a fire, falsely determining a new drug performs similarly to a placebo, or a misinterpretation of campaign attribution leading you to believe a successful campaign experiment was actually a poor test.
| There Is Not A Fire (Null Hypothesis) The Natural State of Things | There Is A Fire (Alternative Hypothesis) The Thing We’re Looking For | |
| Test is Positive (Fire alarm says there’s fire!) |  Type 1 Error, false positive incorrectly rejected the null hypothesis, finding evidence where it did not exist |  correctly reject the null hypothesis we correctly found evidence that H₀ (null hypothesis, default condition) does not explain the test results, yay! |
| Test is Negative (Fire alarm says there is no fire) |  correctly fail to reject the null hypothesis we did not find evidence because it does not exist |  Type 2 Error, false negative incorrectly failed to reject the null hypothesis, failing to find evidence where it did exist |
How Do Statistical Errors Happen?
Limited Sample Size: If the sample size is too small, it may not represent the broader population well, making it more likely that the results won’t be accurate. Solution: Larger samples generally provide a more reliable understanding of the truth.
Sampling Variability: When you take a sample from a population, it’s only one possible subset of the entire group. Each sample might give slightly different results due to natural variation. This variation leads to what are known as random errors. Solution: ensure the way sample measurement is taken does not bias the sample.
Measurement Error: Sometimes, tools or methods used to collect data aren’t perfect. If a measuring instrument is inaccurate or if humans make mistakes during data collection, it can introduce what is known as systematic errors. Solution: validate the way information is collected and how your data is evaluated – making mistakes in interpreting data causes future understanding to be misguided. Validate your information & processes!
Model Assumptions: In understanding data is is often easy to make assumptions (e.g., that data follows a normal distribution, or that relationships between variables are linear). If these assumptions don’t match reality, it can lead to errors in the results. Solution: test and validate your assumptions vs your hypothesis, and be ready to have assumptions that were incorrect!
Random Chance: Sometimes, unusual results simply happen by chance, especially when dealing with probabilities. Even if all procedures are correct, random fluctuations in the data can manifest. Solution: It’s important to rule out random variability from predictable differences in performance, seasonal behavior changes for example. Sample size increases help minimize the effects of random chance.