What are the types of statistical errors?

Before presenting the statistical errors in statistical analysis, it is important to present what is meant by confidence interval, and the related tests:

 Confidence Interval 

In statistical analysis, Confidence Interval refers to the possibility of a parameter that lies within a specified range of values, which is denoted as c. Moreover, the Confidence Interval is connected with the level of significance. The relationship between level of significance and the Confidence Interval is c=1−α.

• The level of significance 0.10 is related to the 90% Confidence Interval.
• The level of significance 0.05 is related to the 95% Confidence Interval.
• The level of significance 0.01 is related to the 99% Confidence Interval.

In statistical analysis, the level of significance is the probability of making the wrong decision when the null hypothesis test is true which is the statistical error. Alpha levels are used in Hypothesis Tests. Usually, these tests are run with an Alpha=0.05, but other levels commonly used are Alpha=0.01 and .10.

In statistical analysis, we were able to determine that our results are statistically significant at the Alpha=0.05 level without using a P-value in statistics. However, when you use the numeric output produced by statistical software, you’ll need to compare the P-value in statistics to your significance level to make this determination.

In statistical analysis, when a P-value in statistics is less than or equal to the level of significance, you reject the null Hypothesis Test. If we take the P-value in statistics for our example and compare it to the common significance levels, it matches the previous graphical results. The P-value in statistics of 0.03112 is statistically significant at an Alpha=0.05, but not at the Alpha=0.01 level.

If we stick to Alpha=0.05, we can conclude that the average energy cost for the population is greater than 260.

Reducing the Alpha level from Alpha=0.05 to Alpha=0.01 reduces the chance of a false positive. to describe the strength of evidence, provide by a p-value in statistics in different categories:

• Alpha > 0.1: No evidence
• Alpha between Alpha=0.05 and Alpha=0.1: Weak evidence
• Alpha between Alpha=0.01 and Alpha=0.05: Evidence
• Alpha between Alpha=0.001 and Alpha=0.01: Strong evidence
• Alpha < 0.001: Very strong evidence

In statistical analysis, lower Alpha levels are sometimes used when you are carrying out multiple tests at the same time in statistical analysis. A common approach is to divide the Alpha level by the number of tests being carried out. For example, if you needed to carry out 5 tests in statistical analysis, you might set your initial Alpha level at Alpha=0.05 then divide it by 5 to obtain the Alpha level of Alpha=0.01.

Although Alpha=0.05 and Alpha=0.01 in statistical analysis are values commonly used for Alpha, there is no overriding mathematical theorem that says these are the only level of significance that we can use in statistical analysis. 

 Why is an Alpha level of .05 commonly used? 

Seeing as the Alpha level is the probability of making a Type 1 error. For example, if we set the Alpha level at 10% then there is large chance that we might incorrectly reject the null Hypothesis Test which is type 1 error, while an Alpha=0.01 would make the area tiny which is not considered type 1 error. So why not use a tiny area instead of the standard Alpha=0.05? to avoid type 1 error.

The smaller the Alpha level, the smaller the area where you would reject the null Hypothesis Test. So, if you have a tiny area, there’s more of a chance that you will NOT reject the null, when in fact you should. This is a Type 2 error.

Statistical error Type 1 

Statistical error type 1 is an error that appears when examining research hypotheses. The Statistical error type 1 is of the first type and is denoted by the alpha α. Statistical error type 1 is the possibility of rejecting the null hypothesis when it is in fact true, and accepts the alternative hypothesis when it is wrong.

That is, the researcher concludes that there is a relationship that does not exist at all. The probability of the Statistical error type 1 = the level of significance (alpha) that has been determined, which is often equal to 0.05.

The reason for Statistical error type 1 may be the lack of representation of the sample in the population, so its average intelligence is higher than the average of the community, or the experimental program, for example, is effective for the sample for some reason, more than it is effective for society.

Statistical error Type 2 

Statistical error Type 2 is an error that appears when examining research hypotheses. And Statistical error Type 2 is denoted by the symbol β (beta). Statistical error Type 2 is the possibility that the researcher will accept the null hypothesis at a time that is - i.e. the null hypothesis - is incorrect, that is, Statistical error Type 2 occurs when we fail to reject the null hypothesis at a time when the alternative hypothesis is correct .

Such as failure to discover the differences between males and females in a variable, although there are significant differences, but the problem is that the sample was unrepresented, or the test method that they were exposed to is inappropriate, or the differences did not appear except by increasing the sample size.

In order to reduce Statistical error Type 2 in statistical analysis, the size of the study sample must be increased. In general, Statistical error Type 2 in statistical analysis is inversely proportional to the Statistical error Type 2 in statistical analysis, meaning that increasing one of them reduces the other.

 Watch: Statistical Errors 

With greetings: Al - Manara Consulting to help researchers and graduate students