A comparison of the means of two groups (1).

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Christian Lawson-Perfect

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8 years, 9 months ago

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Christian Lawson-Perfect 8 years, 9 months ago

Gave some feedback: Ready to use

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Keith McGuinness 9 years, 8 months ago

Created this as a copy of Paired t-test after treatment..

Name	Status	Author	Last Modified
Paired t-test after treatment.	Ready to use	Bill Foster	01/06/2016 09:47
Christian's copy of Paired t-test after treatment.	Ready to use	Christian Lawson-Perfect	01/06/2016 10:06
A comparison of the means of two groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Summary statistics (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (3).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (4).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of four groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Simon's copy of Paired t-test after treatment.	draft	Simon Thomas	05/06/2019 14:44

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Question statement

Suppose that 6 individuals, diagnosed with a particular condition, take part in an experiment that grades their happiness on a scale from 1 to 25 (a higher score is better). They take the test before treatment and then again after treatment with a specific drug. The data is in the table below:

{object}	A	B	C	D	E	F
Before	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$
After	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$

Is there a difference between the average responses before to after?

In other words, test the following null hypothesis:

H0: mean happiness before = mean happiness after.

Give any introductory information the student needs.

			Name	Type	Generated Value

attempt	string	hand
d	list	[ -5, -2, -10, -8, -3, -6 ]
meandiff	number	-5.667
mu1	number	12.5
mu2	number	17.2
object	string	Individual
objects	string	individuals
r1	list	[ 16, 15, 8, 10, 13, 11 ]
r2	list	[ 21, 17, 18, 18, 16, 17 ]
sig1	number	2.2
sig2	number	2.4
stdiff	number	3.011
t95	number	2.571
thismany	integer	6
tcalc	number	-4.610
tupper	number	-4.585
tlower	number	-4.635
mdupper	number	-5.642
mdlower	number	-5.692
stdupper	number	3.036
stdlower	number	2.986
outcome	integer	1
sed	number	1.229

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
'hand'

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `string`

hand

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Find the mean and standard deviations of the difference between the before and after responses

Calculate differences for after response– before response.

Mean of difference = Gap 0. (input to 2 decimal places )

Standard deviation of difference = Gap 1. (input to 2 decimal places)

Now find the paired t-test statistic using the values you have just calculated =Gap 2. (input 2 decimal places)

Is the null hypothesis rejected? Gap 3. Enter 0 for "No" and 1 for "Yes".

Advice

First, recognise that this is a paired t-test: two observations on the same individuals.

So calculate the differences (before $-$ after) between those two observations:

{d}

Note: If you have a graphical calculator, you can enter the before and after observations into two lists (say L1 and L2), then in the heading (title/label) row for L3 type "=L1 $-$ L2" to get the calculator to work out the differences.

Then calculate the mean difference:

{meandiff}

Then the standard deviation (sd) of the differences:

{stdiff}

Note: You should use your calculator to get both the mean and standard deviation.

The standard error (se) is calculated as:

\[ se = \frac{ sd }{ \sqrt{ n }} \]

It is:

{sed}

Finally, calculate the test statisitic, t-calc, as the mean difference divided by the standard error:

\[ t-calc = \frac{ mean difference }{ se} \]

t-calc = {tcalc}

There are 6 subjects, so 5 degrees of freedom, and the test is two-tailed, so the t-table = 2.571.

If t-calc is greater than 2.571, the null is rejected. As this is a two-tailed test, the sign of t-calc (positive or negative) is ignored.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
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A comparison of the means of two groups (1).

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

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Generated value: `string`

Parts

Gap-fill

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Error

A comparison of the means of two groups (1).

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`