Statistics - Chapter 10

Dunnet Test

Dunnet test control familywise error

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F ratios and variances must always be positive in order to calculate

What is the probability of not making a Type I error?

If the probability of making a Type I error is equal to the probability of rejecting the null hypothesis, it stands to reason that the probability of not making a Type I error is equal to the probability of not rejecting the null hypothesis. the probability of not rejecting the null hypothesis when it is true p(not making Type I error) = 1-a(alpha) a=0.05 therefore 1- 0.05 =. 95 .95 is the probability of correctly concluding an effect does not exist

Concerns about controlling type I error

Increases the probability of type II error

When do Type I error occur?

They are the results of random, chance factors.

ANOVA

analysis of variance is statistical procedure to test differences between 2 or more groups

simple comparisons

analytical comparisons between 2 groups

complex comparisons

analytical comparisons between more than 2 groups

analytic comparisons

comparisons between groups that are part of a larger research design

Increasing between group variability

the greater the amount of between-group variability on the decision to reject the null hypothesis

Type II error in not rejecting the null hypothesis

Not rejecting the null hypothesis when the hypothesized effect does exist in the population It occurs when the decision is made to not reject the null hypothesis even though the alternative hypothesis is true

Another name for the probability of not making a type II error?

Statistical power- the probability of not making a type II error

unplanned comparisons

comparisons that have not been build into the research design prior to data collection process "post hoc" comparisons , meaning "after the fact"

planned comparison

comparisons that researchers build into the research design prior to the data collection process "a priori" comparisons which literally means prior to purpose: to test research hypothesis

familywise error

probability of making at least one type I error across a set of comparisons

Extra Notes

Decision to not accept the null hypothesis is not the same as "accept the null hypothesis" There is a lower probability of making a Type I error (.05) than not making a Type I error (.95) Type I error deals with null hypothesis Type II deals with alternative hypothesis.

Within group variability is also known as?

Error variance - variability that cannot be explained or accounted for

What is the probability of making a Type II error?

The probability of making a Type II error, of not rejecting the null hypothesis when we should, is represented by the Greek symbol B (Beta) p(Type II error) = B (Beta) B (Beta) is not equal to 1-a (alpha); this is because type I and type II errors take place under different situations. Extremely difficult to determine the exact probability of making a Type II error because the value of a parameter such as population mean M is unknown when the alternative hypothesis is true

What is the probability of not making a type II error?

The probability of not making a type II error is represented by 1- B (beta) p(not making a type II error) = 1-B (beta)

A measure of effect size

a statistic that measures of the relationship between variables

inappropriateness of highly significant

suggests that analyses at the .01 and .001 level of significance are somehow more noteworthy, meaningful then findings at .05 level Highly significant is inappropriate because statistical significance is dichotomy (significant vs non significant) rather than a continuum

Hypothesis Testing - Defined in Steps

1. A researcher, based on an evaluation of a literature, states a research hypothesis regarding the relationship between variables and collect data to be analyzed 2. At start of a statistical analysis, a null hypothesis, one that states a hypothesized relationship does not exist, is presumed to be true 3. The researcher statically analyzes the collected data 4. Based on the analysis of the data, the researcher makes one of two decisions: reject or do not reject the null hypothesis. if the probability of the value of the statistic calculated from the data is sufficiently low, the null hypothesis is rejected; otherwise the null hypothesis is not rejected.

Why is Type II error a concern?

A Type II error may result in the non-communication of correct information. A Type II error occurs when the null hypothesis isn't rejected and a researcher concludes a difference or relationship doesn't exist; this conclusion implies a study's research hypothesis has not been supported.,

Other ways to describe a type II error

Failing to reject a false null hypothesis Not rejecting the null hypothesis when we should Concluding an effect does not exist when it actually does

Increasing likelihood of rejecting the null hypothesis

Increasing sample size: Larger sample size results in smaller critical values and bigger calculated t static Raising a (alpha): lowers critical values used to make the decision to reject the null hypothesis - which in turn increases the size of region of rejection. Using a directional alternative hypothesis: (one tailed) Increasing the t statistic

Controlling Type I error

It can be reduced by making it more difficult to reject the null hypothesis. More specifically by lowering the value a (alpha), the probability of a statistic needed to reject the null hypothesis.

Expressions of Type I Error

It occurs when the null hypothesis is true but the decision is made to reject the null hypothesis. Rejecting a true null hypothesis Rejecting the null hypothesis when we shouldn't Concluding an effect exists when it actually does not

What is statistical power?

The probability of rejecting the null hypothesis the null hypothesis when the alternative hypothesis is true statistical power of an analysis is the probability of detecting an effect when it does in fact exist in the population

Why is Type I error a concern?

These errors may result in the communication of incorrect information. Consequently, stating that a relationship or effect exists when it does not may adversely impact others thinking, time, energy, and resources. Type I error not only affects researchers, it may also have negatives consequences for a broader audience.

Why does Type II error occur?

They occur when research studies do not find differences or relationships that actually exist in the population. It may result from how researchers conduct their studies.

Review Questions

What are the different ways to describe type I error? Why is the probability of type I error equal to a (alpha)? Why is the probability of not making a type I error equal to 1-a(alpa)? Why is type I error a concern? Why do researchers allow for the possibility of making type I errors?

Interpreting the measures of effect size

a small effect produces rsquared of .01 a medium effect produces rsquared of .06 a large effect produces rsquared of .15 and greater

Cohen's d statistic

estimate of magnitude of the difference between the means of two groups measured in standard deviation units.

What is the probability of making a Type I error?

given that a Type I error only occurs when the decision is made to reject the null hypothesis, the probability of making this type of error is the same as the probability of rejecting the null hypothesis. p(Type I error) = a(alpha) Therefore, the probability of making a Type I error is typically .05 Consequently, in making the decision whether to reject the null hypothesis, there is .05 probability of incorrectly concluding an effect exists when it in fact does not.