Kul 4 2012 t Test Student.1

7/29/2019 Kul 4 2012 t Test Student.1

1/21

The t- test

This test was invented by a called WS Gosset (1867-1937), but preferred to keep anonymous so wrote

under the name Student.

require 2 samples which may be from the same

population.

These samples need not be of equal #, nor are

they paired.

H0: The 2 samples are from the same

population - any differences are due to chance

H1: The 2 samples come from different

populations.


2/21

2

Perbandingan dua nilai tengan (means) Goal: to compare the mean of a numerical variable for

different groups. Tests one categorical vs. one numerical variable

Example:

gender (M, F) vs. height

Paired vs. 2 samplecomparisons

Data from the two groups are

paired

There is a one-to-onecorrespondence between the

individuals in the two groups

Paired designs


3/21

Paired designs

Each member of the pair shares much in common with the

other, exceptfor the tested categorical variable Example: identical twins raised in different environments

Can use the same individual at different points in time

Example: before, after medical treatment

We have many pairs

In each pair, there is one member that has one treatmentand another who has another treatment

Treatment can mean group

Paired comparisons - setup

To compare two groups, we use the mean of the

difference between the two members of each pair


4/21

STUDENTS T TEST

The students t test is used to see if to sets of data differ significantly.

The method assumes that the results follow the normal distribution (also

called student's t-distribution) if the null hypothesis is true.

This null hypothesis will usually stipulate that there is no significant

difference between the means of the two data sets.

It is best used to try and determine whether there is a difference between

two independent sample groups. For the test to be applicable, the sample

groups must be completely independent, and it is best used when the sample

size is too small to use more advanced methods.

Before using this type of test it is essential to plot the sample data from he

two samples and make sure that it has a reasonably normal distribution, or

the students t test will not be suitable.

It is also desirable to randomly assign samples to the groups, whereverpossible.
http://www.experiment-resources.com/significance-test.htmlhttp://www.experiment-resources.com/null-hypothesis.htmlhttp://www.experiment-resources.com/null-hypothesis.htmlhttp://www.experiment-resources.com/significance-test.html


5/21

The Use of the Null Hypothesis Is the difference in two sample populations due to chance or a

real statistical difference? The null hypothesis assumes that there will be no difference

or no change or no effect of the experimental treatment.

If treatment A is no better than treatment B then the nullhypothesis is supported.

If there is a significant difference between A and B then thenull hypothesis is rejected...

Test statistic > critical value

P < alpha

Reject the null hypothesis

Statistically significant


6/21


7/21


8/21

Sample

Null hypothesis

The population mean

is equal to o

One-sample t-test

Test statistic

t= Yo

s /n

Null distribution

t with n-1 dfcompare

How unusual is this test statistic?

P < 0.05 P > 0.05

Reject Ho Fail to reject Ho


9/21

T-test

T-test determines the probability that the null

hypothesis concerning the means of two small

samples is correct

The probability that two samples are

representative of a single population

(supporting null hypothesis) OR two different

populations (rejecting null hypothesis)


10/21

The theory...You have 2 samples which may be from 1

distribution or 2. To assess the likelihood, find

how many s.d.s the means of the 2 populations

are apart:

How many S.D.s?

Calculate t = (1 - 2) / pooled sd

12

The t test is a parametric test - it

assumes the data are normally

distributed.


11/21

21

21

2

21

22

2

11

21

2

)1()1(

nn

nn

nn

snsn

XXt

Two Sample Difference of Means T-Test

2

21

22

2

11

2

)1()1(

nn

snsnSp2 =Pooled variance of the two groups

21

21

nnnn = common standard deviation of two groups

The nominator of the equation captures difference in

means,

while the denominator captures the variation within

and between each group


12/21

Contoh

Test on verbal test scores by gender:Females: mean = 50.9, variance = 47.553, n=6

Males: mean =41.5, variance = 49.544, n=10

)10(6

106

2106

544.49)110(553.47)16(

5.419.50t

)26667(.826.484.9

t

02.134.9t 605.2

608.34.9 t

Now what do we do with this obtained

value?


13/21

Steps of Testing and Significance

1. Statement of null hypothesis: if there is not one then how can you be

wrong?

2. Set Alpha Level of Risk: .10, .05, .01

3. Selection of appropriate test statistic: T-test.

4. Computation of statistical value: get obtained value.

5. Compare obtained value to critical value:6. Comparison of the obtained and critical values.

7. If obtained value is more extreme than critical value, you may reject

the null hypothesis. In other words, you have significant results.

8. If point seven above is not true, obtained is lower than critical, then

null is not rejected.


14/21

T table of values (5% = 0.05)For example:For 10 degrees of freedom

(2N-2)

The chart value to compare

your t value to is 2.228

If your calculated t value is

between

+2.228 and -2.228

Then accept the null

hypothesis the mean are

similar

If your t value falls outside

+2.228 and -2.228 (larger

than 2.228 or smaller than -

2.228)

Fail to reject the null

hypothesis (accept the

alternative hypothesis) there

is a significant difference.


15/21


16/21


17/21


18/21


19/21


20/21


21/21

Kul 4 2012 t Test Student.1

Documents

Transcript of Kul 4 2012 t Test Student.1