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I would like to carry out statistical analysis of multiple sets of data using Student's $t$-test. The problem definition is given below:

I have compiled experimental data from several literature sources pertaining to measurement of voltage (y-axis) as a function of temperature (x-axis). Measurements were carried out using two experimental techniques, Method I and II. Data from literature 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}

Each of the experimental data can (or should) be fitted to a linear equation i.e $y=mx+c$. Now I have the following doubt: 1). Is it possible to use Student's $t$-test to statistically compare the data sets and find out which of them are consistent or in agreement with each other?

Any suggestions or hints on this problem would be helpful.

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1 Answer 1

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You have more than one statistical question wrapped up as one bundle. Shortcuts won't help.

For this type of question, you will likely get the most mileage out of ANOVA tools/analysis. Any ANOVA can be done as regression with enough dummy variables, but ANOVA (analysis of variance) and ANCOVA (analysis of co-variance) is easier to understand initially. Search "ANOVA" and "ANCOVA" and see if that helps.

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