Statistical Errors
Even in the best research project, there is always a possibility that the researcher will make a mistake regarding the relationship between the two variables. This mistake is called statistical error.
In statistical test theory the notion of statistical error is an integral part of hypothesis testing. The test requires an unambiguous statement of a null hypothesis, which usually corresponds to a default
"state of nature", for example "this person is healthy", "this accused is not guilty" or "this product is not broken". An alternative hypothesis is the negation of null hypothesis, for example, "this person is not healthy",
"this accused is guilty" or "this product is broken". The result of the test may be negative, relative to null hypothesis (not healthy, guilty, broken) or positive (healthy, not guilty, not broken). If the result of the test corresponds with reality, then a correct decision has been made.
However, if the result of the test does not correspond with reality, then an error has occurred. Due to the statistical nature of a test, the result is never, except in very rare cases, free of error. Two types of error are distinguished: type I error and type II error.
In statistics, a type I error (or error of the first kind) is the incorrect rejection of a true null hypothesis. A type 11 error (or error of the second kind) is the failure to reject a -false. null hypothesis. A type I error is a false positive. Usually a type I error leads one to conclude that a thing or relationship exists when really it doesn't, for example, that a
patient has a disease being tested for when really the patient does not have the disease, or that a medical treatment cures a disease when really it doesn't. A type II error is a false negative. Examples of type II errors would be a blood test failing to detect the disease it was designed to detect, in a patient who really has the disease; or a clinical trial of a medical treatment failing to show that the treatment works when really it does. When comparing two means, concluding the means were different when in reality they were not different would be a Type I error;
concluding the means were not different when in reality they were different would be a 'Type II error.
All statistical hypothesis tests have a probability of making type I and type II errors. For example, all blood tests for a disease will falsely detect the disease in some proportion of people who don't have it, and will fail to detect the disease in some proportion of people who do have it. A test's probability of making a type I error is denoted by a. A test's probability of making a type II error is denoted by β.
The detail is given below:
Type-I Error:
The first is called a Type I error. This occurs when the researcher assumes that a relationship exists when in fact the evidence is that it does not. In a Type 1 error, the researcher should accept the null hypothesis and reject the research hypothesis, but the opposite occurs.
The probability of committing a Type I error is called alpha (a).
A type I error, also known as an error of the first kind, occurs when the null hypothesis (H0) is true, but is rejected. It is asserting something that is absent, a false hit. A type I error may be compared with a so-called false positive (a result that indicates that a given condition is present when it actually is not present) in tests where a single condition is tested for. Type I errors are philosophically a focus of skepticism and Occam's razor. A Type I error occurs when we believe a falsehood. In terms of folk tales, an investigator may be "crying wolf' without a wolf in sight (raising a false alarm) (Ho: no wolf).
The rate of the type I error is called the size of the test and denoted by the Greek letter a (alpha). -It usually equals the significance level of a test. In the case of a simple null hypothesis a is the probability of a type I error. If the null hypothesis is composite, a is the maximum (supremum) of the possible probabilities of a type I error.
Explanation:
A Type I Error is also known as a False Positive or Alpha Error.
This happens when you reject the Null Hypothesis even if it is true. The Null Hypothesis is simply a statement that is the opposite of your hypothesis. For example, you think that boys are better in arithmetic than girls. Your null hypothesis would be: "Boys are not better than girls in arithmetic."
You will make a Type I Error if you conclude that boys are better than girls in arithmetic when in reality, there is no difference in how boys and girls perform. In this case, you should accept the null hypothesis since there is no real difference between the two groups when it comes to arithmetic ability. If you reject the null hypothesis and say that one group is better, then you are making a Type I Error.
Type-II Error
The second is called a Type II error. This occurs when the researcher assumes that a relationship does not exist when in fact the evidence is that it does. In a Type II error, the researcher should reject the null hypothesis and accept the research hypothesis, but the opposite occurs. The probability of committing a Type II error is called beta.
Generally, reducing the possibility of committing a Type I error increases the possibility of committing a Type II error and vice versa, reducing the possibility of committing a Type II error increases the possibility of committing a Type I error.
Researchers generally try to minimize Type I errors, because when a researcher assumes a relationship exists when one really does not, things may be worse off than before. In Type II errors, the researcher
misses an opportunity to confirm that a relationship exists, but is no worse off than before.
Type II Error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one accepts a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance.
A type II error accepts the null hypothesis, although the alternative hypothesis is the true state of nature. It confirms an idea that should have been rejected, claiming that two observances are the same, even though they are different.
Example:
An example of a type II error would be a pregnancy test that gives a negative result, even though the woman is in fact pregnant. In this example, the null hypothesis would be that the woman is not pregnant, and the alternative hypothesis is that she is pregnant.
In other words, a type DI error, also known as an error of the second kind, occurs when the null hypothesis is false, but erroneously fails to be rejected. It is failing to assert what is present, a miss. A type II error may be compared with a so-called false negative (where an actual 'hit' was disregarded by the test and seen as a 'miss') in a test checking for a single condition with a definitive result of true or false. A Type II error is committed when we fail to believe a truth. In terms of folk tales, an investigator may fail to see the wolf ("failing to raise an alarm"). Again, Ho: no wolf.
The rate of the type II error is denoted by the Greek letter f3 (beta) and related to the power of a test (which equals 143).
What we actually call type I or type H error depends directly on the null hypothesis. Negation of the null hypothesis causes type I and type II errors to switch roles.
The goal of the test is to determine if the null hypothesis can be rejected. A statistical test can either reject (prove false) or fail to reject
(fail to prove false) a null hypothesis, but never prove it true (i.e., failing to reject a null hypothesis does not prove it true).
Explanation:
A Type II Error is also known as a False Negative or Beta Error.
This happens when you accept the Null Hypothesis when you should in fact reject it. The Null Hypothesis is simply a statement that is the opposite of your hypothesis. For example, you think that dog owners are friendlier than cat owners. Your null hypothesis would be: "Dog owners are as friendly as cat owners."
You will make a Type II Error if dog owners are actually friendlier than cat owners, and yet you conclude that both kinds of pet owners have the same level of friendliness. In this case, you should reject the null hypothesis since there is a real difference in friendliness between the two groups. If you accept the null hypothesis and say that both types of pet owners are equally friendly, then you are making a Type II Error.