Lecture 6: Research & Null Hypothesis

p=.0001

(significant at .001 level

p=.03

(significant at .05 level

Null/Statistical Hypothesis

A hypothesis of "no difference or no relationship

Type I error

Also known as an "error of the first kind", an α error, or a "false positive": the error of rejecting a null hypothesis when it is actually true

Research Hypothesis

An "educated guess" or tentative proposition regarding the possible solution or explanation to the problem being studied

Research Hypothesis: Directionality examples

Ex:1 Subjects who participate in the newly devised training program will decrease their 40 yard dash time. (directional). Ex:2 Male and female students at GCSU will significantly differ in the number of calories consumed per day. (non-directional).

Null Hypothesis example

For example, if we want to compare the test scores of two random samples of men and women, a null hypothesis would be that the mean score of the male population was not different than the mean score of the female population:

Another way to represent the null hypothesis?

H0 H0 : μ1 = μ2

Example when .05 is not set by the investigator

In some studies, such as those in the pharmaceutical industry, .05 would be considered too high of level of error. In which case, a smaller alpha would be chosen such as .01 or .001.

For example..

In the case of our pharmaceutical drug, it would make sense to set the alpha level at .01 or .001 as opposed to .05, because there may be side effects associated with the drug or other implications . . . even through setting the alpha at .001 actually increases the type II error rate. This risk may be warranted.

Unidirectional hypothesis

Researcher has no reason to believe that a difference or relation exists in any direction.

Directional hypothesis

Researcher has reason to believe that a particular relationship or difference exists between groups or subjects according to a particular direction.

Level of Significance

The rejection of a hypothesis (or failure to do so) is based upon a level of significance (alpha level, α), which corresponds to the area in the critical region of a chart.

Null Hypothesis

The statistical hypothesis that one variable (e.g. whether or not a study participant was allocated to receive an intervention) has no association with another variable or set of variables, or that two or more population distributions do not differ from one another. In simplest terms, the null hypothesis states that the results observed in a study are no different from what might have occurred as a result of the play of chance.

Null Hypothesis Example

There will be no difference in 40 yard dash time between subjects who participate in the training program and those who do not.

Comparing Type I and II Errors

Type I errors typically lead to changes that are unwarranted. Type II errors typically lead to a maintenance of the status quo when a change is warranted. The consequences of a Type I error are generally considered more serious than the consequences of a Type II error, although there are certainly exceptions.

Rejecting the null hypothesis at the <.05 level suggests...

a 95% probability that the difference between the two variables is real (or statistically significant), that is, not the result of chance.

Type II error

also known as an "error of the second kind", a β error, or a "false negative": the error of accepting a null hypothesis when the alternative hypothesis is the true state of nature

Many research efforts in health/physical activity establish the level of significance at what?

at the 5% (.05) alpha level, although there are circumstances in which it could be different.

What are they designated by? What are needed to calculate it?

beta (β). Complex computations are need to calculate it.

Primarily used for...

statistical testing.

What does it state?

that the independent variable has no effect on the dependent variable

Type I error rates are set by,,

the investigator, usually at .05

μ1

the mean of population 1

μ2

the mean of population 2

The alpha level is...

the probability of committing a type I error.

R1

the research hypothesis

Usually based on..

theory and previous research

In other words...

there is a less than 5% probability that the differences are caused by error or chance.

In other words...

this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none

In other words..

this is the error of failing to observe a difference when in truth there is one. This type of error can only occur when the statistician accepts the null hypothesis

R1=directional

μ1 < μ2 μ1 > μ2

R1=non-directional

μ1 ≠ μ2