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Chapter 6Statistical Significance

- By Vanessa Cortes
- Darlene Villafranca

Significant means reliable not important

- In normal English, "significant" means important,

while in Statistics "significant" means probably

true (not due to chance). - A research finding may be true without being

important. - When statisticians say a result is "highly

significant" they mean it is very probably true. - They do not (necessarily) mean it is highly

important.

Statistics vs. Parameters

- Characterized aspects of data that constitute a

sample Statistics - Characterized features of data that constitute a

populationParameters - Researchers want to know if the sampling

descriptive statistics accurately approximates

population parameters

Three types of Significance

- Statistical Significance
- Practical Significance
- Clinical Significance
- All require calculations
- All yield numerical results

Statistical Significance Inferential Statistics

- Inferential Statistics are often the next step

after you have collected summarized data - Inferential statistics are used to make

inferences from smaller group of data to possibly

larger one - Inferential statistics are used to infer

something about the population based on the

samples characteristics

Null Hypothesis

- Null is always a statement of equality
- Null can be true or false
- No difference or truly is an inequality
- Null applies ONLY to the population
- The researcher never really knows the Null

hypothesis and if there is or is not a difference

between groups - WHY?

Hypothesis Testing

- You cannot make both Type I and Type II Error on

a given hypothesis - Once you reject, you could not have made a Type

II error. - Once you fail to reject, you could not have made

Type I error. - Hypotheses predicting zero differences or zero

relationship

Accept or Reject the Null Hypothesis

Statistical Power

- The power of a statistical test is the

probability that the test will reject a false

null hypothesis (that it will not make a Type II

error). As power increases, the chances of a Type

II error decrease, and vice versa. The

probability of a Type II error is referred to as

ß. Therefore power is equal to 1 - ß.

One-Tailed and Two-Tailed Significance Tests

- One important concept in significance testing is

whether you use a one-tailed or two-tailed test

of significance. The answer is that it depends on

your hypothesis. When your research hypothesis

states the direction of the difference or

relationship, then you use a one-tailed

probability. For example, a one-tailed test would

be used to test these null hypotheses Females

will not score significantly higher than males on

an IQ test. Blue collar workers are will not buy

significantly more product than white collar

workers. Superman is not significantly stronger

than the average person. In each case, the null

hypothesis (indirectly) predicts the direction of

the difference.

Two-Tailed Significance Tests

- A two-tailed test would be used to test these

null hypotheses There will be no significant

difference in IQ scores between males and

females. There will be no significant difference

in the amount of product purchased between blue

collar and white collar workers. There is no

significant difference in strength between

Superman and the average person. The one-tailed

probability is exactly half the value of the

two-tailed probability.

Properties of Sampling Distributions

- For all sampling distributions, the standard

deviation of the sampling distribution gets

smaller as sample size increases. - The mean of the statistics in a sampling

distribution for unbiased estimators will equal

the population parameter being estimated

Standard Error/Sampling Error

- Standard deviation of the sampling

distributionStandard error of the statistic or

Standard error. (SE)

Inferentially

- Statistical significance test is to divide the

statistic by its standard error. - 3 synonymous names for the fundamental ratio
- 1. t statistic
- 2. critical ratio
- 3. Wald statistic

Test Statistics

- Test statisticsstandardized sampling

distributions - Test statistics (TS) distributions can be used in

place of P values . - The comparison of a given P calculated with a

given PCRITICAL will always yield the same

decision about the comparison of a given TS

calculated with a given TSCRITICAL.

P calculated

- P calculated is calculating the estimated

probability - P values range from 0 to 1
- or 0 to 100

Procedure Used to Test for Significance

- Whenever we perform a significance test, it

involves comparing a test value that we have

calculated to some critical value for the

statistic. It doesn't matter what type of

statistic we are calculating (e.g., a

t-statistic, a chi-square statistic, an

F-statistic, etc.), the procedure to test for

significance is the same. - 1. Decide on the critical alpha level you will

use (i.e., the error rate you are willing to

accept). - 2. Conduct the research.
- 3. Calculate the statistic.
- 4. Compare the statistic to a critical value

obtained from a table.

If your statistic is higher than the critical

value from the table

- Your finding is significant.
- You reject the null hypothesis.
- The probability is small that the difference or

relationship happened by chance, and p is less

than the critical alpha level (p lt alpha ).

If your statistic is lower than the critical

value from the table

- Your finding is not significant.
- You fail to reject the null hypothesis.
- The probability is high that the difference or

relationship happened by chance, and p is greater

than the critical alpha level (p gt alpha ).