## Introduction to statistical data analysis

September 06, 2011 at 03:25 PM | categories: statistics | View Comments

## Contents

## Introduction to statistical data analysis

John Kitchin

```
clear all
clc
```

## Problem statement.

Given several measurements of a single quantity, determine the average value of the measurements, the standard deviation of the measurements and the 95% confidence interval for the average.

## the data

y = [8.1 8.0 8.1];

## the average and standard deviation

ybar = mean(y); s = std(y);

## the confidence interval

This is a recipe for computing the confidence interval. The strategy is: 1. compute the average 2. Compute the standard deviation of your data 3. Define the confidence interval, e.g. 95% = 0.95 4. compute the student-t multiplier. This is a function of the confidence interval you specify, and the number of data points you have minus 1. You subtract 1 because one degree of freedom is lost from calculating the average. The confidence interval is defined as ybar +- T_multiplier*std/sqrt(n).

ci = 0.95; alpha = 1 - ci; n = length(y); %number of elements in the data vector T_multiplier = tinv(1-alpha/2, n-1); ci95 = T_multiplier*s/sqrt(n); % confidence interval [ybar - ci95, ybar + ci95] % we can say with 95% confidence that the true mean lies between these two % values.

ans = 7.9232 8.2101

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