Solved – How to Normalize data

anovacovariancemultivariate normal distributionnormalization

In a study, the baseline data are recorded (blood pressure, BP1) prior to the experiment (watching a horror film). After the experiment, the data (BP2) are collected again. The problem is that not all participants arrived in the lab with the same level of blood pressure. Therefore it is important to normalize the data before doing the analysis.

I have seen some researchers apply log to standardize the data. I am not clear what log does and the procedure involved.

What is the best solution in this case?
Please advise the statistical test that needs to be performed in this case to normalize the data.

Best Answer

This question may be approached in several different ways.

As pointed out by dnbwise you could simply use changes in blood pressure ([BP] at time 2 minus BP at time 1), or ratios (BP at time 2 divided by BP at time 1). Otherwise, you could simply run a paired t test or paired Wilcoxon signed-rank test. Other meaningful strategies could be to create a bootstrapped estimate of BP at time 2.

I would favor though using a regression approach in which you have BP at time 1 as independent variable and BP at time 2 as independent variable.

This approach is eminently feasible with several different approaches in many packages (eg 'gee' in R), and its great strength is that you can upgrade it as you need adding terms for other independent variables (eg age, gender, movie title), and so forth.

Related Solutions

Normalization – How to Normalize Data to 0-1 Range?

If you want to normalize your data, you can do so as you suggest and simply calculate the following:

$$z_i=\frac{x_i-\min(x)}{\max(x)-\min(x)}$$

where $x=(x_1,...,x_n)$ and $z_i$ is now your $i^{th}$ normalized data. As a proof of concept (although you did not ask for it) here is some R code and accompanying graph to illustrate this point:

enter image description here

# Example Data
x = sample(-100:100, 50)

#Normalized Data
normalized = (x-min(x))/(max(x)-min(x))

# Histogram of example data and normalized data
par(mfrow=c(1,2))
hist(x,          breaks=10, xlab="Data",            col="lightblue", main="")
hist(normalized, breaks=10, xlab="Normalized Data", col="lightblue", main="")