Basic Statistical Analysis in MATLAB Get Certified

MATLAB provides powerful tools for statistical analysis, enabling users to compute descriptive statistics, perform hypothesis testing, analyze data trends, and visualize results. This section covers common statistical operations with examples and outputs.

Descriptive Statistics

MATLAB makes it simple to compute basic statistics like mean, median, variance, and standard deviation:

% Sample Data
data = [12, 15, 20, 22, 25, 28, 30];

% Calculate Mean
mean_val = mean(data);
disp(['Mean: ' num2str(mean_val)]);

% Calculate Median
median_val = median(data);
disp(['Median: ' num2str(median_val)]);

% Calculate Variance
var_val = var(data);
disp(['Variance: ' num2str(var_val)]);

% Calculate Standard Deviation
std_val = std(data);
disp(['Standard Deviation: ' num2str(std_val)]);

Expected output:

Mean: 21.7143
Median: 22
Variance: 42.5714
Standard Deviation: 6.5255

Data Summarization

You can quickly summarise datasets using built-in functions such as sum, min and max:

% Summarizing data
data = [12, 15, 20, 22, 25, 28, 30];

data_sum = sum(data);
disp(['Sum: ' num2str(data_sum)]);

data_min = min(data);
disp(['Minimum: ' num2str(data_min)]);

data_max = max(data);
disp(['Maximum: ' num2str(data_max)]);

Expected output:

Sum: 152
Minimum: 12
Maximum: 30

Correlation and Covariance

Correlation and covariance measure the relationship between two datasets:

% Sample Data
x = [1, 2, 3, 4, 5];
y = [2, 4, 6, 8, 10];

% Calculate Correlation
corr_val = corrcoef(x, y);
disp('Correlation Matrix:');
disp(corr_val);

% Calculate Covariance
cov_val = cov(x, y);
disp('Covariance Matrix:');
disp(cov_val);

Expected output:

Correlation Matrix:
    1.0000    1.0000
    1.0000    1.0000

Covariance Matrix:
    2.5000    5.0000
    5.0000   10.0000

Probability Distributions

Probability distributions such as the normal and uniform distributions are commonly used in statistical modelling:

% Generating Normally Distributed Random Numbers
normal_data = randn(1, 1000);
disp('Generated Normal Distribution Data');
disp(normal_data(1:5));   % first 5 values

% Generating Uniformly Distributed Random Numbers
uniform_data = rand(1, 1000);
disp('Generated Uniform Distribution Data');
disp(uniform_data(1:5));  % first 5 values

% Display Histogram
histogram(normal_data);
title('Normal Distribution');

A histogram representing normally distributed random numbers will be displayed. Experiment with different datasets to observe varying distributions.

Hypothesis Testing

MATLAB allows you to perform hypothesis testing, such as the t-test, to validate assumptions about datasets:

% Sample Data
data1 = [2.3, 3.1, 3.8, 4.5, 5.2];
data2 = [2.1, 3.0, 3.5, 4.7, 5.0];

% Perform t-test
[h, p] = ttest(data1, data2);
disp(['Hypothesis Test Result (h): ' num2str(h)]);
disp(['p-value: ' num2str(p)]);

Expected output:

Hypothesis Test Result (h): 0
p-value: 0.5642

The output suggests no significant difference between the two datasets, as the p-value is greater than 0.05.

Useful MATLAB Functions for Statistical Analysis

Practice Questions