T-Test with Minitab 16 Assistant menu and interpretation

8/13/2019 T-Test with Minitab 16 Assistant menu and interpretation

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Minitab Project ReportApplication of Assistant (one sample t-test)

Statistics is challenging but with Minitab Assistant Menu we can easily analyze our dataand conveniently interpret the results. The Assistant Menu use commonly usedstatistical tools and provide guidance to help you choose the right statistical tools. The

most distinctive feature of Assistant menu is its capability of interpreting the statisticalresults which has been a nightmare for the social scientists in the past.

Example: The height of all students of PYP follows a normal distribution. Ten students chosen at

random and their heights are recorded in inches are 63, 63, 66, 67, 68, 69, 70, 70, 71, 71. In the

light of these data, discuss the suggestion that the mean height of all PYP students is 66 inches.

Step:1 From the menu go to Assistant > Graphical Analysis (a note will appear telling what all

is there is Graphical analysis).


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Press Graphic Analysis a pop-up

option box Choose a Graphical

Analysis will appear.

Take the cursor to Graphical

Summary it will be highlighted

click it and another dialogue box will pop-up.

This is

the

Graphical

Summary

dialogue

box.

Move the

variable

Height

to the

space Y

column:

Then

press

OK.

You will see a Summary for Height

appearing on the screen. This gives the bar

chart of the data along with the normal curve

and some descriptive statistics coupled with

normality tests in the right panel. Below the


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graph are the

confidence

intervals of mean

and the median. So

we can say that this

option gives us all

in one summary

statistics.

Now let us ask the Assistant how to go for one sample t-test. Follow the screen shoot on the right

and

click:Hypothesis

Test.

A pop-up option dialogue box will appear take

the cursor on 1-sample t and click then a

1-Sample t Testdialogue box will appear.


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The salient features of the summary report are the p-value, Statistics portion and the first

comment in the comments portion.

from the target (p > 0.05).

The mean of Height is not significantly different

> 0.50.10

NoYes

P = 0.091

7068666462

66

between 65.646 and 69.954.

confident that the true mean is

from sample data. You can be 95%

associated with estimating the mean

-- CI: Quantifies the uncertainty

at the 0.05 level of significance.

conclude that the mean differs from 66

-- Test: There is not enough evidence to

Sample size 10

Mean 67.8

95% CI (65.646, 69.954)

Standard deviation 3.0111Target 66

Statistics

1-Sample t Test for the Mean of HeightSummary Report

Does the mean differ from 66?

Distribution of Data

Where are the data relative to the target?

Comments

To put it in a nut shell the summary reports tell us that since theP-value (0.09) is greater than

Alpha level (0.05) therefore we do not reject the Null Hypothesis Ho: = 66.


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The Diagnostic report is generated if you entered the differencevalue in the 1sample t-Test

discussed on the previous page. This report tells us that in order to observe the difference as large

as 1.5 then the sample should be of size 34 students instead of 10 students and then we will be

80% chance of rejecting the Ho:=66.

75

70

65

60

difference.

direction, you would have a 29.1% chance of detecting the

If the true mean differed from the target by 1.5 in either

For alpha = 0.05 and sample size = 10:

100%

3.4765

90%

2.3633

60%< 40%

1.5

22 60.0

27 70.034 80.0

45 90.0

Sample Size Power

difference of 1.5?

What sample size is required to detect a

10 29.1

Your Sample

Data in Worksheet Order

Investigate outliers (marked in red).

Power

What is the chance of detecting a difference?

Difference of interest: 1.5

Power is a function of the sample size and the standard deviation. If the power is not satisfactory, consider increasing the sample size.

1-Sample t Test for the Mean of Height

Diagnostic Report

The third report card -provides assumption checks to warn us when our analysis may be suspect

i.e. not as good as they should have been -is not produced instead a conclusion and the

highlighted text box is produced for the users convenience.


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Conclusion: Since the p-value is greater than 0.05 level of significance therefore the null

hypothesis Ho: =66 cannot be rejected and we may conclude that the population mean height

of PYP students is 66 inches.

What if our null hypothesis is in fact false and the mean height is actually greater than 66.

From the past records it has been estimated that the mean height of PYP students is 67.5

inches. Keeping in view the past records the researcher suggests that the population

average height is 67.5. So now, the question arises how large a sample be selected in order

to reject the false null hypothesis. For this we need to do power analysis which is shown in

the second graph. Power means the probability of rejecting a false null hypothesis and is

denoted by 1-. The Graph suggests that we need a sample of 34 students to achieve the

power of 0.80 i.e. to get an 80% chance of rejecting a false null hypothesis we must select a

sample of 34 PYP students. Therefore, having a small sample in fact increases our type -II

error i.e. accepting a false null hypothesis when in fact our alternative hypothesis is true. In

other words type-II () error can be controlled by increasing the sample size.

T-Test with Minitab 16 Assistant menu and interpretation

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