Analysis using Student's $t$-test
$begingroup$
I would like to carry out statistical analysis of data using Student's t-test. The problem definition is given below:
I have compiled experimental data from several sources pertaining to measuring voltage (y-axis) as a function of temperature (x-axis). Measurements were carried out using two methods I and II. Data are presented below
Data: Source 1 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.54 \
694 & -2.517 \
723 & -2.508 \
hline
end{array}
Data: Source 2 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
708 & -2.618 \
733 & -2.612 \
758 & -2.599 \
783 & -2.587 \
808 & -2.577 \
833 & -2.564 \
hline
end{array}
Data: Source 3 (Method 1)
begin{array} {c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.493 \
748 & -2.48 \
773 & -2.466 \
798 & -2.453 \
823 & -2.439 \
848 & -2.427 \
873 & -2.415 \
898 & -2.402 \
925 & -2.386 \
hline
end{array}
Data: Source 4 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.541 \
773 & -2.514 \
823 & -2.487 \
hline
end{array}
Data: Source 5 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.561 \
673 & -2.588 \
673 & -2.58 \
703 & -2.547 \
703 & -2.571 \
703 & -2.572 \
773 & -2.491 \
773 & -2.516 \
773 & -2.518 \
823 & -2.437 \
823 & -2.481 \
823 & -2.469 \
hline
end{array}
I have the following queries:
1). Can we use student's t-test to compare which of the data sets are consistent with each other?
2). If we assume that in terms of accuracy of experimental method/technique, Method 1 is more accurate than Method 2, and we give 60% weightage to Method 1 data sets and 40 % weightage to Method 2 datasets, can we include this weightage in student's t-test for analysis.
I have performed the following analysis:
1). Use Method 1 datasets and carry out least squares fitting to obtain $y=m_{1}x+c_{1}$ and Method 2 datasets to obtain $y=m_{2}x+c_{2}$.
2). Use the weightage factors to obtain the final expression for the linear fit i.e.
$y=(0.6m_{1}+0.4m_{2})x + (0.6c_{1}+0.4c_{2})$
From the point of view of statistical analysis of data fitting, is this method correct? This method however does not answer the question I have posed above.
Thank you for any suggestions and hints on this problem
statistics
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
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add a comment |
$begingroup$
I would like to carry out statistical analysis of data using Student's t-test. The problem definition is given below:
I have compiled experimental data from several sources pertaining to measuring voltage (y-axis) as a function of temperature (x-axis). Measurements were carried out using two methods I and II. Data are presented below
Data: Source 1 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.54 \
694 & -2.517 \
723 & -2.508 \
hline
end{array}
Data: Source 2 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
708 & -2.618 \
733 & -2.612 \
758 & -2.599 \
783 & -2.587 \
808 & -2.577 \
833 & -2.564 \
hline
end{array}
Data: Source 3 (Method 1)
begin{array} {c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.493 \
748 & -2.48 \
773 & -2.466 \
798 & -2.453 \
823 & -2.439 \
848 & -2.427 \
873 & -2.415 \
898 & -2.402 \
925 & -2.386 \
hline
end{array}
Data: Source 4 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.541 \
773 & -2.514 \
823 & -2.487 \
hline
end{array}
Data: Source 5 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.561 \
673 & -2.588 \
673 & -2.58 \
703 & -2.547 \
703 & -2.571 \
703 & -2.572 \
773 & -2.491 \
773 & -2.516 \
773 & -2.518 \
823 & -2.437 \
823 & -2.481 \
823 & -2.469 \
hline
end{array}
I have the following queries:
1). Can we use student's t-test to compare which of the data sets are consistent with each other?
2). If we assume that in terms of accuracy of experimental method/technique, Method 1 is more accurate than Method 2, and we give 60% weightage to Method 1 data sets and 40 % weightage to Method 2 datasets, can we include this weightage in student's t-test for analysis.
I have performed the following analysis:
1). Use Method 1 datasets and carry out least squares fitting to obtain $y=m_{1}x+c_{1}$ and Method 2 datasets to obtain $y=m_{2}x+c_{2}$.
2). Use the weightage factors to obtain the final expression for the linear fit i.e.
$y=(0.6m_{1}+0.4m_{2})x + (0.6c_{1}+0.4c_{2})$
From the point of view of statistical analysis of data fitting, is this method correct? This method however does not answer the question I have posed above.
Thank you for any suggestions and hints on this problem
statistics
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
$endgroup$
$begingroup$
You might find help here stats.stackexchange.com
$endgroup$
– mm-crj
Dec 29 '18 at 17:19
add a comment |
$begingroup$
I would like to carry out statistical analysis of data using Student's t-test. The problem definition is given below:
I have compiled experimental data from several sources pertaining to measuring voltage (y-axis) as a function of temperature (x-axis). Measurements were carried out using two methods I and II. Data are presented below
Data: Source 1 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.54 \
694 & -2.517 \
723 & -2.508 \
hline
end{array}
Data: Source 2 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
708 & -2.618 \
733 & -2.612 \
758 & -2.599 \
783 & -2.587 \
808 & -2.577 \
833 & -2.564 \
hline
end{array}
Data: Source 3 (Method 1)
begin{array} {c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.493 \
748 & -2.48 \
773 & -2.466 \
798 & -2.453 \
823 & -2.439 \
848 & -2.427 \
873 & -2.415 \
898 & -2.402 \
925 & -2.386 \
hline
end{array}
Data: Source 4 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.541 \
773 & -2.514 \
823 & -2.487 \
hline
end{array}
Data: Source 5 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.561 \
673 & -2.588 \
673 & -2.58 \
703 & -2.547 \
703 & -2.571 \
703 & -2.572 \
773 & -2.491 \
773 & -2.516 \
773 & -2.518 \
823 & -2.437 \
823 & -2.481 \
823 & -2.469 \
hline
end{array}
I have the following queries:
1). Can we use student's t-test to compare which of the data sets are consistent with each other?
2). If we assume that in terms of accuracy of experimental method/technique, Method 1 is more accurate than Method 2, and we give 60% weightage to Method 1 data sets and 40 % weightage to Method 2 datasets, can we include this weightage in student's t-test for analysis.
I have performed the following analysis:
1). Use Method 1 datasets and carry out least squares fitting to obtain $y=m_{1}x+c_{1}$ and Method 2 datasets to obtain $y=m_{2}x+c_{2}$.
2). Use the weightage factors to obtain the final expression for the linear fit i.e.
$y=(0.6m_{1}+0.4m_{2})x + (0.6c_{1}+0.4c_{2})$
From the point of view of statistical analysis of data fitting, is this method correct? This method however does not answer the question I have posed above.
Thank you for any suggestions and hints on this problem
statistics
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
$endgroup$
I would like to carry out statistical analysis of data using Student's t-test. The problem definition is given below:
I have compiled experimental data from several sources pertaining to measuring voltage (y-axis) as a function of temperature (x-axis). Measurements were carried out using two methods I and II. Data are presented below
Data: Source 1 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.54 \
694 & -2.517 \
723 & -2.508 \
hline
end{array}
Data: Source 2 (Method 1)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
708 & -2.618 \
733 & -2.612 \
758 & -2.599 \
783 & -2.587 \
808 & -2.577 \
833 & -2.564 \
hline
end{array}
Data: Source 3 (Method 1)
begin{array} {c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.493 \
748 & -2.48 \
773 & -2.466 \
798 & -2.453 \
823 & -2.439 \
848 & -2.427 \
873 & -2.415 \
898 & -2.402 \
925 & -2.386 \
hline
end{array}
Data: Source 4 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
723 & -2.541 \
773 & -2.514 \
823 & -2.487 \
hline
end{array}
Data: Source 5 (Method 2)
begin{array}{c|c}
hline
Temperature(K) & Voltage (V) \
hline
673 & -2.561 \
673 & -2.588 \
673 & -2.58 \
703 & -2.547 \
703 & -2.571 \
703 & -2.572 \
773 & -2.491 \
773 & -2.516 \
773 & -2.518 \
823 & -2.437 \
823 & -2.481 \
823 & -2.469 \
hline
end{array}
I have the following queries:
1). Can we use student's t-test to compare which of the data sets are consistent with each other?
2). If we assume that in terms of accuracy of experimental method/technique, Method 1 is more accurate than Method 2, and we give 60% weightage to Method 1 data sets and 40 % weightage to Method 2 datasets, can we include this weightage in student's t-test for analysis.
I have performed the following analysis:
1). Use Method 1 datasets and carry out least squares fitting to obtain $y=m_{1}x+c_{1}$ and Method 2 datasets to obtain $y=m_{2}x+c_{2}$.
2). Use the weightage factors to obtain the final expression for the linear fit i.e.
$y=(0.6m_{1}+0.4m_{2})x + (0.6c_{1}+0.4c_{2})$
From the point of view of statistical analysis of data fitting, is this method correct? This method however does not answer the question I have posed above.
Thank you for any suggestions and hints on this problem
statistics
statistics
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
asked Dec 29 '18 at 16:22
Suddhasattwa Ghosh Suddhasattwa Ghosh
13
13
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You might find help here stats.stackexchange.com
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– mm-crj
Dec 29 '18 at 17:19
add a comment |
$begingroup$
You might find help here stats.stackexchange.com
$endgroup$
– mm-crj
Dec 29 '18 at 17:19
$begingroup$
You might find help here stats.stackexchange.com
$endgroup$
– mm-crj
Dec 29 '18 at 17:19
$begingroup$
You might find help here stats.stackexchange.com
$endgroup$
– mm-crj
Dec 29 '18 at 17:19
add a comment |
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You might find help here stats.stackexchange.com
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– mm-crj
Dec 29 '18 at 17:19