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### Practical Statistics

Mean Comparisons

There are six statistics that will

answer90% of all questions!

- Descriptive
- Chi-square
- Z-tests
- Comparison of Means
- Correlation
- Regression

t-test come in three types:

- A sample mean against a hypothesis.

t-test come in three types:

- A sample mean against a hypothesis.
- Two sample means compared to each other.

t-test come in three types:

- A sample mean against a hypothesis.
- Two sample means compared to each other.
- Two means within the same sample.

The standard error for means is:

Hence for one mean compared to a hypothesis:

Each t value comes with a certain degree

of freedom df = n - 1

IQ has a mean of 100 and a standard deviation of

15. Suppose a group of immigrants came into

London. A random sample of 400 of these

Immigrants found an average IQ of 98.

Does this group have an IQ below the

population average?

The test statistic looks like this:

There are n – 1 = 399 degrees of freedom.

The results are printed out by a computer or looked

up on a t-test table.

up on the internet….

http://www.danielsoper.com/statcalc/calc08.aspx

For the IQ test: t(399) = 2.67, p = 0.00395

Since the test was “one-tailed,” the critical value

of t would be -1.65.

Therefore, t(399) = -2.67 would indicate

that the immigrants IQ is below normal.

t-test come in three types:

- A sample mean against a hypothesis.
- Two sample means compared to each other.
- Two means within the same sample.

Suppose that a new product was test marketed in

the United States and in Japan. The company

hypothesizes that customers in both countries

would consume the product at the same rate.

A sample of 500 in the U.S. used an average of 200 kilograms

a year (sd = 20), while a sample of 400 in Japan used an

average of 180 kilograms a year (sd = 25).

Test the hypothesize…..

The results would be written as:

(t(898) = 0.89, ns),

and the conclusion is

that there is no difference in the consumption rate between the U.S. and Japanese customers.

Can you see why?

It is caused by a common mistake of

confusing the sampling distribution

with a the sample distribution.

(t(898) = 13.33, p < .0001),

and the conclusion is that there is a large difference in the consumption rate between the U.S. and Japanese customers.

t-test come in three types:

- A sample mean against a hypothesis.
- Two sample means compared to each other.
- Two means within the same sample.

t-test come in three types:

3. Two means within the same sample.

This t-test is used with correlated samples and/or

when the same person or object is measured

twice in the same sample.

Tom 89 90 1

Jan 88 91 3

Jason 87 86 -1

Halley 90 90 0

Bill 75 79 4

The measurement of interest is d.

Examples can be found at these sites:

http://en.wikipedia.org/wiki/T-test

http://canhelpyou.com/statistics/tTestDependentSamples.html

Suppose there are more than two groups

that need to be compared.

The t-test cannot be utilized for two reason.

- The number of pairs becomes large.

Suppose there are more than two groups

that need to be compared.

The t-test cannot be utilized for two reason.

- The number of pairs becomes large.
- The probability of t is no longer accurate.

Compares the means of two or more groups

by comparing the variance between groups

with the variance that exists within groups.

F is the ratio of variance:

http://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVAhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

The F-test http://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

http://www.statsoft.com/textbook/distribution-tables/

The F-testhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

The probability distribution is dependent upon

the degrees of freedom between and the

degrees of freedom within.

The F-testhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Typical output looks like this:

In SPSS http://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVAANOVA looks like this:

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

The average age of Iowans over 18 is

approximately 47. Is the sample a cross-section

of this population by age?

A sample mean against a hypothesis.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is the measure of personality different between

men and women?

Two sample means compared to each other.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is the measure of personality different between

men and women?

Two sample means compared to each other.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is the measure of personality different between

men and women?

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Do respondents like themselves better than the

service provider?

Two means within the same sample.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Do respondents like themselves better than the

service provider?

Two means within the same sample.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is the measure of personality different between

shopping times?

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is personality difference by perception of

service encounter?

More than two sample means compared to each other.

Service Encounterhttp://controls.engin.umich.edu/wiki/index.php/Factor_analysis_and_ANOVA

Is personality difference by perception of

service encounter?

More than two sample means compared to each other.

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