Question

Examples of Graphical Analysis Techniques in Research [WLO: 2] [CLOs: 2, 3]

Locate an example of a research study that uses graphs and/or tables in its analysis. Explain what this statistical technique allows the researchers to accomplish and/or conclude in the study. Note: Graphic presentations are most often found in the Results section of a study.

Answer 1

Consider the following data which shows the distance of 9 planets from a star, and the corresponding chart:

Position No.	Distance from star
1	35
2	67
3	98
4	137
5	483
6	987
7	1789
8	2808
9	3686

4 10 0 6 Position

We see that the position and the distance from star are not correlated, as there seems to be a non-linear relationship between the two. Hence we perform a log-transformation on the distance to check if we can linearize the data and then perform a linear regression. Position no. vs Log(Distance) data and chart are as below:

Position No.	log(Distance)
1	1.5441
2	1.8261
3	1.9912
4	2.1367
5	2.6839
6	2.9943
7	3.2526
8	3.4484
9	3.5666

4.0000 3.5000 3.0000 2.5000 th 2.0000 1.5000 1.0000 0.5000 0.0000 10 Position

Hence, the graph looks quite linear now, and we can go ahead and fit a linear regression model on the above data. Doing this in Excel (go to Data tab -> Data analysis -> Regression,choose Position no. as X-column and Distance from star as Y-column), we get the following output:

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.243439519	0.083721832	14.85203436	1.50331E-06	1.045468846	1.441410193
Position No.	0.272288019	0.01487776	18.30168125	3.6007E-07	0.237107708	0.307468331

Hence, we get the regression model as:

Distance = 1.2434 + 0.2723 * Position

Given the low p-value of the position coefficient (<< 0.05), the linear relationship is very significant now.

This is an example of linear transformation of data in statistics to make it fit for linear regression. Hope it helps!