Hypothesis tests use sample data to make inferences about the properties of a population. You gain tremendous benefits by working with random samples because it is usually impossible to measure the entire population.
However, there are tradeoffs when you use samples. The samples we use are typically a minuscule percentage of the entire population. Consequently, they occasionally misrepresent the population severely enough to cause hypothesis tests to make errors.
In this blog post, you will learn about the two types of errors in hypothesis testing, their causes, and how to manage them.
Potential Outcomes in Hypothesis Testing
Hypothesis testing is a procedure in inferential statistics that assesses two mutually exclusive theories about the properties of a population. For a generic hypothesis test, the two hypotheses are as follows:
- Null hypothesis: There is no effect
- Alternative hypothesis: There is an effect.
The sample data must provide sufficient evidence to reject the null hypothesis and conclude that the effect exists in the population. Ideally,a hypothesis test fails to reject the null hypothesis when the effect is not present in the population, and it rejects the null hypothesis when the effect exists.
Statisticians define two types of errors in hypothesis testing. Creatively, they call these errors Type I and Type II errors. Both types of error relate to incorrect conclusions about the null hypothesis.
The table summarizes the four possible outcomes for a hypothesis test.
Test Rejects Null | Test Fails to Reject Null | |
Null is True | Type I Error False Positive | Correct decision No effect |
Null is False | Correct decision Effect exists | Type II error False negative |
Related post: How Hypothesis Tests Work: P-values and the Significance Level
Fire alarm analogy for the types of errors
A fire alarm provides a good analogy for the types of hypothesis testing errors. Preferably, the alarm rings when there is a fire and does not ring in the absence of a fire. However, if the alarm rings when there is no fire, it is a false positive, or a Type I error in statistical terms. Conversely, if the fire alarm fails to ring when there is a fire, it is a false negative, or a Type II error.
Using hypothesis tests correctly improves your chances of drawing trustworthy conclusions. However, errors are bound to occur.
Unlike the fire alarm analogy, there is no sure way to determine whether an error occurred after you perform a hypothesis test. Typically, a clearer picture develops over time as other researchers conduct similar studies and an overall pattern of results appears. Seeing how your results fit in with similar studies is a crucial step in assessing your study’s findings.
Now, let’s take a look at each type of error in more depth.
Type I Errors: False Positives
When you see a p-value that is less than your significance level, you get excited because your results are statistically significant. However, it could be a type I error. The supposed effect might not exist in the population. Again, there is usually no warning when this occurs.
Why do these errors occur? It comes down to sample error. Your random sample has overestimated the effect by chance. It was the luck of the draw. This type of error doesn’t indicate that the researchers did anything wrong. The experimental design, data collection, data validity, and statistical analysis can all be correct, and yet this type of error still occurs.
Even though we don’t know for sure which studies have false positive results, we do know their rate of occurrence. The rate of occurrence for Type I errors equals the significance level of the hypothesis test, which is also known as alpha (α).
The significance level is an evidentiary standard that you set to determine whether your sample data are strong enough to reject the null hypothesis. Hypothesis tests define that standard using the probability of rejecting a null hypothesis that is actually true. You set this value based on your willingness to risk a false positive.
Related post: How to Interpret P-values Correctly
Using the significance level to set the Type I error rate
When the significance level is 0.05 and the null hypothesis is true, there is a 5% chance that the test will reject the null hypothesis incorrectly. If you set alpha to 0.01, there is a 1% of a false positive. If 5% is good, then 1% seems even better, right? As you’ll see, there is a tradeoff between Type I and Type II errors. If you hold everything else constant, as you reduce the chance for a false positive, you increase the opportunity for a false negative.
Type I errors are relatively straightforward. The math is beyond the scope of this article, but statisticians designed hypothesis tests to incorporate everything that affects this error rate so that you can specify it for your studies. As long as your experimental design is sound, you collect valid data, and the data satisfy the assumptions of the hypothesis test, the Type I error rate equals the significance level that you specify. However, if there is a problem in one of those areas, it can affect the false positive rate.
Warning about a potential misinterpretation of Type I errors and the Significance Level
When the null hypothesis is correct for the population, the probability that a test produces a false positive equals the significance level. However, when you look at a statistically significant test result, you cannot state that there is a 5% chance that it represents a false positive.
Why is that the case? Imagine that we perform 100 studies on a population where the null hypothesis is true. If we use a significance level of 0.05, we’d expect that five of the studies will produce statistically significant results—false positives. Afterward, when we go to look at those significant studies, what is the probability that each one is a false positive? Not 5 percent but 100%!
That scenario also illustrates a point that I made earlier. The true picture becomes more evident after repeated experimentation. Given the pattern of results that are predominantly not significant, it is unlikely that an effect exists in the population.
Type II Errors: False Negatives
When you perform a hypothesis test and your p-value is greater than your significance level, your results are not statistically significant. That’s disappointing because your sample provides insufficient evidence for concluding that the effect you’re studying exists in the population. However, there is a chance that the effect is present in the population even though the test results don’t support it. If that’s the case, you’ve just experienced a Type II error. The probability of making a Type II error is known as beta (β).
What causes Type II errors? Whereas Type I errors are caused by one thing, sample error, there are a host of possible reasons for Type II errors—small effect sizes, small sample sizes, and high data variability. Furthermore, unlike Type I errors, you can’t set the Type II error rate for your analysis. Instead, the best that you can do is estimate it before you begin your study by approximating properties of the alternative hypothesis that you’re studying. When you do this type of estimation, it’s called power analysis.
To estimate the Type II error rate, you create a hypothetical probability distribution that represents the properties of a true alternative hypothesis. However, when you’re performing a hypothesis test, you typically don’t know which hypothesis is true, much less the specific properties of the distribution for the alternative hypothesis. Consequently, the true Type II error rate is usually unknown!
Type II errors and the power of the analysis
The Type II error rate (beta) is the probability of a false negative. Therefore, the inverse of Type II errors is the probability of correctly detecting an effect. Statisticians refer to this concept as the power of a hypothesis test. Consequently, 1 – β = the statistical power. Analysts typically estimate power rather than beta directly.
If you read my post about power and sample size analysis, you know that the three factors that affect power are sample size, variability in the population, and the effect size. As you design your experiment, you can enter estimates of these three factors into statistical software and it calculates the estimated power for your test.
Suppose you perform a power analysis for an upcoming study and calculate an estimated power of 90%. For this study, the estimated Type II error rate is 10% (1 – 0.9). Keep in mind that variability and effect size are based on estimates and guesses. Consequently, power and the Type II error rate are just estimates rather than something you set directly. These estimates are only as good as the inputs into your power analysis.
Low variability and larger effect sizes decrease the Type II error rate, which increases the statistical power. However, researchers usually have less control over those aspects of a hypothesis test. Typically, researchers have the most control over sample size, making it the critical way to manage your Type II error rate. Holding everything else constant, increasing the sample size reduces the Type II error rate and increases power.
Learn more about Power in Statistics.
Graphing Type I and Type II Errors
The graph below illustrates the two types of errors using two sampling distributions. The critical region line represents the point at which you reject or fail to reject the null hypothesis. Of course, when you perform the hypothesis test, you don’t know which hypothesis is correct. And, the properties of the distribution for the alternative hypothesis are usually unknown. However, use this graph to understand the general nature of these errors and how they are related.
The distribution on the left represents the null hypothesis. If the null hypothesis is true, you only need to worry about Type I errors, which is the shaded portion of the null hypothesis distribution. The rest of the null distribution represents the correct decision of failing to reject the null.
On the other hand, if the alternative hypothesis is true, you need to worry about Type II errors. The shaded region on the alternative hypothesis distribution represents the Type II error rate. The rest of the alternative distribution represents the probability of correctly detecting an effect—power.
Moving the critical value line is equivalent to changing the significance level. If you move the line to the left, you’re increasing the significance level (e.g., α 0.05 to 0.10). Holding everything else constant, this adjustment increases the Type I error rate while reducing the Type II error rate. Moving the line to the right reduces the significance level (e.g., α 0.05 to 0.01), which decreases the Type I error rate but increases the type II error rate.
Is One Error Worse Than the Other?
As you’ve seen, the nature of the two types of error, their causes, and the certainty of their rates of occurrence are all very different.
A common question is whether one type of error is worse than the other? Statisticians designed hypothesis tests to control Type I errors while Type II errors are much less defined. Consequently, many statisticians state that it is better to fail to detect an effect when it exists than it is to conclude an effect exists when it doesn’t. That is to say, there is a tendency to assume that Type I errors are worse.
However, reality is more complex than that. You should carefully consider the consequences of each type of error for your specific test.
Suppose you are assessing the strength of a new jet engine part that is under consideration. Peoples lives are riding on the part’s strength. A false negative in this scenario merely means that the part is strong enough but the test fails to detect it. This situation does not put anyone’s life at risk. On the other hand, Type I errors are worse in this situation because they indicate the part is strong enough when it is not.
Now suppose that the jet engine part is already in use but there are concerns about it failing. In this case, you want the test to be more sensitive to detecting problems even at the risk of false positives. Type II errors are worse in this scenario because the test fails to recognize the problem and leaves these problematic parts in use for longer.
Using hypothesis tests effectively requires that you understand their error rates. By setting the significance level and estimating your test’s power, you can manage both error rates so they meet your requirements.
The error rates in this post are all for individual tests. If you need to perform multiple comparisons, such as comparing group means in ANOVA, you’ll need to use post hoc tests to control the experiment-wise error rate.
Related
FAQs
What are the types of errors in hypothesis testing? ›
In the framework of hypothesis tests there are two types of errors: Type I error and type II error. A type I error occurs if a true null hypothesis is rejected (a “false positive”), while a type II error occurs if a false null hypothesis is not rejected (a “false negative”).
Which type of error is more serious in hypothesis testing? ›Hence, type error is considered to be worse or more dangerous than type because to reject what is true is more harmful than keeping the data that is not true.
How many types of errors can be made when testing a hypothesis * 1 point? ›The two types of errors that are possible in hypothesis testing are called type 1 and type 2 errors. These errors result in incorrect conclusions.
What is a Type 3 error in hypothesis testing? ›Fundamentally, type III errors occur when researchers provide the right answer to the wrong question, i.e. when the correct hypothesis is rejected but for the wrong reason.
What are the main types of errors? ›...
Systematic Errors:
- Environmental Errors.
- Observational Errors.
- Instrumental Errors.
Generally errors are classified into three types: systematic errors, random errors and blunders.
Which error is more harmful? ›Now, generally in societies, Type 1 error is more dangerous than Type 2 error because you are convicting the innocent person. But if you can see then Type 2 error is also dangerous because freeing a guilty can bring more chaos in societies because now the guilty can do more harm to society.
What type of error is hardest to identify? ›Logical Errors
Logical errors are the hardest of all error types to detect. They do not cause the program to crash or simply not work at all, they cause it to “misbehave” in some way, rendering wrong output of some kind. One example of a logic error is null reference.
Type 1 error control is more important than Type 2 error control, because inflating Type 1 errors will very quickly leave you with evidence that is too weak to be convincing support for your hypothesis, while inflating Type 2 errors will do so more slowly.
How many types of errors can be made when interpreting statistical results? ›Statisticians define two types of errors in hypothesis testing. Creatively, they call these errors Type I and Type II errors. Both types of error relate to incorrect conclusions about the null hypothesis.
How do you determine Type 1 and Type 2 errors? ›
A type 1 error occurs when you wrongly reject the null hypothesis (i.e. you think you found a significant effect when there really isn't one). A type 2 error occurs when you wrongly fail to reject the null hypothesis (i.e. you miss a significant effect that is really there).
How many errors does an experiment have? ›There are two main types of experimental error that scientists and non-scientists alike must be aware of: systematic errors and random errors.
What is Type 4 error? ›A type IV error was defined as the incorrect interpretation of a correctly rejected null hypothesis. Statistically significant interactions were classified in one of the following categories: (1) correct interpretation, (2) cell mean interpretation, (3) main effect interpretation, or (4) no interpretation.
What is Type 2 error in hypothesis? ›A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population.
What is Type 3 and Type 4 error? ›A Type III error is directly related to a Type IV error; it's actually a specific type of Type III error. When you correctly reject the null hypothesis, but make a mistake interpreting the results, you have committed a Type IV error.
What are the 3 types of errors? ›- (1) Systematic errors. With this type of error, the measured value is biased due to a specific cause. ...
- (2) Random errors. This type of error is caused by random circumstances during the measurement process.
- (3) Negligent errors.
- Systematic Error. Systematic errors come from identifiable sources. ...
- Random Error. Random errors are the result of unpredictable changes. ...
- Human Error. Human errors are a nice way of saying carelessness.
Some common errors are with prepositions most importantly, subject verb agreement, tenses, punctuation, spelling and other parts of speech. Prepositions are tricky, confusing and significant in sentence construction.
What are 3 sources of error in an experiment? ›Common sources of error include instrumental, environmental, procedural, and human. All of these errors can be either random or systematic depending on how they affect the results.
What type of error is accuracy? ›Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other.
What are the 7 types of systematic errors? ›
- Equipment. Inaccurate equipment such as an poorly calibrated scale.
- Environment. Environmental factors such as temperature variations that cause incorrect readings of the volume of a liquid.
- Processes. ...
- Calculations. ...
- Software. ...
- Data Sources. ...
- Data Processing.
The best-known error-detection method is called parity, where a single extra bit is added to each byte of data and assigned a value of 1 or 0, typically according to whether there is an even or odd number of "1" bits.
What is a good range of error? ›For a good measurement system, the accuracy error should be within 5% and precision error should within 10%.
Which error is more serious sampling or non-sampling? ›Non-sampling errors are more serious than sampling errors because a sampling error can be minimised by taking a larger sample but it is difficult to minimise non-sampling error, even by taking a large sample. Even a Census can contain non-sampling errors.
What is worse systematic or random error? ›Systematic errors are much more problematic than random errors because they can skew your data to lead you to false conclusions. If you have systematic error, your measurements will be biased away from the true values.
Which error Cannot be revealed? ›- Errors of omission. An error of omission refers to a mistake where the accountant skipped the entry in its entirety. ...
- Errors of Commission. ...
- Errors of Principle. ...
- Compensating Errors. ...
- Complete reversal errors. ...
- Transportation errors. ...
- Duplication errors.
Logic errors typically are the most difficult type of errors to find and correct. Finding logic errors is the primary goal of testing.
Is a bigger standard error better? ›Standard error measures the amount of discrepancy that can be expected in a sample estimate compared to the true value in the population. Therefore, the smaller the standard error the better.
Is a higher standard error better? ›A measure of the (in)accuracy of the statistic. A standard error of 0 means that the statistic has no random error. The bigger the standard error, the less accurate the statistic.
Is Type 1 or Type 2 error more important? ›Type 1 error control is more important than Type 2 error control, because inflating Type 1 errors will very quickly leave you with evidence that is too weak to be convincing support for your hypothesis, while inflating Type 2 errors will do so more slowly.
How many standard errors are there? ›
There are five types of standard error which are: Standard error of the mean. Standard error of measurement. Standard error of the proportion.
What will happen if the researcher increases the level of Type I error without making any other changes? ›If we were to increase the level of Type 1 error, this means that we are increasing our significance level. In contrast, if we had a lower significance level, we would have to see an observed value very, very different from what we expected in our study in order to reject the null hypothesis.
How many errors are there in statistics? ›Data can be affected by two types of error: sampling error and non-sampling error.
Why is it important to understand type 1 and type 2 errors? ›As you analyze your own data and test hypotheses, understanding the difference between Type I and Type II errors is extremely important, because there's a risk of making each type of error in every analysis, and the amount of risk is in your control.
How do you determine Type 2 error? ›How to Calculate the Probability of a Type II Error for a Specific Significance Test when Given the Power. Step 1: Identify the given power value. Step 2: Use the formula 1 - Power = P(Type II Error) to calculate the probability of the Type II Error.
Does sample size affect type 1 error? ›Small or large sample size does not affect type I error. So sample size will not increase the occurrence of Type I error. The only principle is that your test has a normal sample size. If the sample size is small in Type II errors, the level of significance will decrease.
How do you evaluate errors? ›- Subtract the actual value from the expected value. First, subtract the actual value from the expected value. ...
- Divide by the actual value. After you find the difference between the actual and expected value, you can divide the result of the calculation by the actual value. ...
- Multiply the value by 100.
There are three steps in error analysis of most experiments. The first, propagation of errors, can be performed even before the experiment is performed. The second, measuring the errors, is done during the experiment. And the third, comparison with accepted values, is performed after the experiment is completed.
What is a good experimental error? ›Engineers also need to be careful; although some engineering measurements have been made with fantastic accuracy (e.g., the speed of light is 299,792,458 1 m/sec.), for most an error of less than 1 percent is considered good, and for a few one must use advanced experimental design and analysis techniques to get any ...
What are Type 1 errors called? ›A type 1 error is also known as a false positive and occurs when a researcher incorrectly rejects a true null hypothesis. This means that your report that your findings are significant when in fact they have occurred by chance.
What is a Type 3 test? ›
Type III tests examine the significance of each partial effect, that is, the significance of an effect with all the other effects in the model. They are computed by constructing a type III hypothesis matrix L and then computing statistics associated with the hypothesis L. = 0.
What is a Type 2 error example? ›A type II error produces a false negative, also known as an error of omission. For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.
What is the probability of a Type 1 error? ›Type 1 errors have a probability of “α” correlated to the level of confidence that you set. A test with a 95% confidence level means that there is a 5% chance of getting a type 1 error.
Is Type 2 error the p value? ›In fact, for that same parameter value, P(Type 2 error)=1−Power . In a courtroom, a Type 2 error is acquitting a guilty person. A Type 1 error is when you incorrectly reject the null when it is true.
What causes type1 error? ›What causes type 1 errors? Type 1 errors can result from two sources: random chance and improper research techniques. Random chance: no random sample, whether it's a pre-election poll or an A/B test, can ever perfectly represent the population it intends to describe.
What is Type 1 Type 2 Type 3 error? ›Type I error: "rejecting the null hypothesis when it is true". Type II error: "failing to reject the null hypothesis when it is false". Type III error: "correctly rejecting the null hypothesis for the wrong reason".
How many types error are there? ›Generally errors are classified into three types: systematic errors, random errors and blunders.
What is a Type 3 statistical error? ›Another definition is that a Type III error occurs when you correctly conclude that the two groups are statistically different, but you are wrong about the direction of the difference.
What are the 3 major types of error in error analysis? ›Researchers have identified three broad types of error analysis according to the size of the sample. These types are: massive, specific and incidental samples.
What are Type 1 and Type 2 errors in hypothesis testing? ›In statistics, a Type I error means rejecting the null hypothesis when it's actually true, while a Type II error means failing to reject the null hypothesis when it's actually false.
What are the 2 types of errors? ›
As a consequence there are actually two different types of error here. If we reject a null hypothesis that is actually true, then we have made a type I error. On the other hand, if we retain the null hypothesis when it is in fact false, then we have made a type II error.
Is there a type 3 error in statistics? ›A type III error is where you correctly reject the null hypothesis, but it's rejected for the wrong reason. This compares to a Type I error (incorrectly rejecting the null hypothesis) and a Type II error (not rejecting the null when you should).
What are the five 5 different types of error detection techniques? ›Error Detecting Techniques:
Single parity check. Two-dimensional parity check. Checksum. Cyclic redundancy check.
- Errors of principle, and.
- Clerical Errors. Errors of Omission. Errors of Commission.
- Compensating Errors.
So here's the mnemonic: first, a Type I error can be viewed as a "false alarm" while a Type II error as a "missed detection"; second, note that the phrase "false alarm" has fewer letters than "missed detection," and analogously the numeral 1 (for Type I error) is smaller than 2 (for Type I error).
Which error is better type 1 or 2? ›Now, generally in societies, Type 1 error is more dangerous than Type 2 error because you are convicting the innocent person. But if you can see then Type 2 error is also dangerous because freeing a guilty can bring more chaos in societies because now the guilty can do more harm to society.
What is a Type 2 error also known as? ›A type II error, also known as an error of the second kind or a beta error, confirms an idea that should have been rejected, such as, for instance, claiming that two observances are the same, despite them being different.
Why do Type 2 errors occur? ›Type II error is mainly caused by the statistical power of a test being low. A Type II error will occur if the statistical test is not powerful enough. The size of the sample can also lead to a Type I error because the outcome of the test will be affected.
What is random and systematic error? ›Random error introduces variability between different measurements of the same thing, while systematic error skews your measurement away from the true value in a specific direction.