STANDARD ERRORS

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STANDARD ERRORS

Standard Error
The standard error of the mean (SEM) is the standard deviation of the sample mean estimate of a population mean.
Sampling Error
The difference between sample and population values.
Type I Error
The probability of rejecting a null hypothesis when it is true.
Type II Error
The probability of accepting a null hypothesis when it is false.
Type III error
Type III errors occur when researchers provide the right answer to the wrong question.
Type IV error
Type IV errors occur when researchers provide the wrong answer to the right question.


Level of Significance
An integral part of every quantitative research study is the need to determine an appropriate statistical significance level, alpha, also referred to as critical. Before data are collected, this level should be selected (a priori) because this level is logical, and the information gleaned from rejecting the null hypothesis is meaningful. In medical studies, it is common to set the significance level to p < .01, whereas p < .05 is common in the social sciences. For comparison, a recalculated or Test Statistic calculation is used. The decision is the same regardless of whether a recalculated or Test Statistic calculation is used.
The risk set by the researcher for rejecting a null hypothesis when it is true. The level of significance has certain conventional values associated with it, such as .01 and .05. 
For example, if the level of significance is .01, it means that on any one test of the null hypothesis, there is a chance the null hypothesis will be rejected, when it is true- leading to the conclusion [that there is a group difference when there really is no group difference]. 
If the level of significance is .05, it means that on any one test of the null hypothesis, there is a chance, it will be rejected. When the null is true-leading to the conclusion [that there is a group difference] when there really is no group difference. 
Notice that the level of significance is associated with an independent test of the null, and it is not appropriate to say that " on 100 tests of the null hypothesis, I will make errors on only 5."
In a research report, statistical significance is usually represented as p .05, read as the probability of observing that the outcome is less than .05, and often expressed in a report or journal article simply as " significant at the .05 level."
Degrees of freedom
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move without violating any constraint imposed on it, is called degree of freedom.

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