Simon's copy of Paired t-test after treatment.

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Simon Thomas 5 years, 9 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 15 individuals, diagnosed with bipolar disorder take part in an experiment that grades their happiness on a scale from 1 to 25. They take the test before treatment and then again after a specific drug has been prescribed. The data is shown below:

{object}	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
Before	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$	$\var{r1[8]}$	$\var{r1[9]}$	$\var{r1[10]}$	$\var{r1[11]}$	$\var{r1[12]}$	$\var{r1[13]}$	$\var{r1[14]}$
After	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$	$\var{r2[8]}$	$\var{r2[9]}$	$\var{r2[10]}$	$\var{r2[11]}$	$\var{r2[12]}$	$\var{r2[13]}$	$\var{r2[14]}$

Is there a difference between the average responses of the two groups?

In order to answer this, complete the following questions.

Give any introductory information the student needs.

			Name	Type	Generated Value

attempt	string	hand
cmsg	list	List of 5 items
d	list	List of 15 items
meandiff	number	5.333
msg	list	List of 5 items
mu1	number	14
mu2	number	18
object	string	Individual
objects	string	individuals
pmsg	list	List of 5 items
pvalue	number	0.000
r1	list	List of 15 items
r2	list	List of 15 items
sig1	number	2.4
sig2	number	2.4
stdiff	number	3.244
t	integer	0
t90	number	1.761
t95	number	2.145
t99	number	2.977
t999	number	4.14
thismany	integer	15
tvalue	number	6.367
v	list	[ 1, 0, 0, 0, 0 ]

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

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) Choose one from a list
Part c) Choose one from a list

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 3 decimal places )

Standard deviation of difference = Gap 1. (input to 3 decimal places)

Now find the paired t-test statistic using the values you have just calculated =Gap 2. (3 decimal places)

Advice

The table of differences is given by:

{object}	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
Before	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$	$\var{r1[8]}$	$\var{r1[9]}$	$\var{r1[10]}$	$\var{r1[11]}$	$\var{r1[12]}$	$\var{r1[13]}$	$\var{r1[14]}$
After	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$	$\var{r2[8]}$	$\var{r2[9]}$	$\var{r2[10]}$	$\var{r2[11]}$	$\var{r2[12]}$	$\var{r2[13]}$	$\var{r2[14]}$
Differences	$\var{d[0]}$	$\var{d[1]}$	$\var{d[2]}$	$\var{d[3]}$	$\var{d[4]}$	$\var{d[5]}$	$\var{d[6]}$	$\var{d[7]}$	$\var{d[8]}$	$\var{d[9]}$	$\var{d[10]}$	$\var{d[11]}$	$\var{d[12]}$	$\var{d[13]}$	$\var{d[14]}$

The mean of the differences is $\overline{x_d}=\var{meandiff}$.

The variance $V$ of the differences is
\[\begin{eqnarray*} V&=&\frac{1}{14}\left(\simplify[]{{d[0]^2}+{d[1]^2}+{d[2]^2}+{d[3]^2}+{d[4]^2}+{d[5]^2}+{d[6]^2}+{d[7]^2}+{d[8]^2}+{d[9]^2}+{d[10]^2}+{d[11]^2}+{d[12]^2}+{d[13]^2}+{d[14]^2}}-15\times \var{meandiff}^2\right)\\ &=&\var{variance(d)} \end{eqnarray*} \]
Hence we have the standard deviation $s_d= \sqrt{V}=\var{stdiff}$ to 3 decimal places.

The paired t-statistic is given by:

\[t_d=\frac{\overline{x_d}-\mu_d}{\frac{s_d}{\sqrt{n}}}\]

In this example $n=15$ and the null hypothesis is that the means are the same i.e. $\mu_d=0$.

On calculating we find $t_d=\var{tvalue}$.

Looking up this value on the T-distribution table for $t_{14}$

\[\begin{array}{r|rrrrr}&0.20&0.10&0.05&0.01&0.001\\\hline14&1.345&1.761&2.145&2.977&4.140\end{array}\]

We see that the t-statistic {msg[t]} and the table tells us that the $p$ value {pmsg[t]}.

Hence we conclude that {cmsg[t]}.

Give a worked solution to the whole question.

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Simon's copy of Paired t-test after treatment.

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Taxonomy: mathcentre

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Simon Thomas 5 years, 9 months ago

Error in variable testing condition

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Generated value: `string`

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Simon's copy of Paired t-test after treatment.

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`