Data Evaluation and Comparisons

Introduction

Basics of Excel™

Basic Statistics

Linear Regression

Data Evaluation & Comparison

Introduction

Hypotheses

t-test

1- and 2-Tailed Tests

F-test

Summary

Introduction
→   Presentation of data comparison techniques, and the steps for evaluating set of data
Hypotheses
→   Definition of statistical hypotheses about datasets
t-tests
→   t-tests for comparing the means of different datasets
One- & Two-tailed tests
→   Testing whether a mean is greater than, less than, or not equal to, another mean
F-test
→   Testing differences between standard deviations of datasets, for comparing precision

You have now seen how to generate a calibration curve for an instrument from a set of linear data, and then use the curve to determine the concentration of an unknown sample from a measured signal.

Let's say you just taken a number of concentration readings from a sample of unknown concentration, and you want to determine whether the difference between your measured value and the stated value is statistically significant, or simply do to a random error. Or that you measured the same sample with two different methods, but got two different concentration readings, and you want to determine whether the difference is due to random error, or if your methods are not equivalent. Statistical tests of significance, which are covered in this section, can be used to answer this sort of question.

In general, statistical tests are used for comparing two means or two standard deviations to see if they are significantly different. You can also compare a mean from measured data to an accepted value to see if your sample measurements match the literature values.

There are a few steps for evaluating a dataset or comparing multiple sets of data. These steps are summarized in the following list:

1. Decide which test to perform - t-test for comparing means, and F-test for comparing standard deviations.
2. Choose a confidence level P, decide if the test should be 1- or 2-tailed, and determine the number of degrees of freedom.
3. Define the hypothesis as to whether your means or standard deviations are significantly different. You should define a null hypothesis and an alternate hypothesis.
4. Compute the test statistic using the appropriate formula, for either the t-test or the F-test.
5. Compare the test statistic to the tabulated value. Depending on whether the calculated value is greater than or less than the tabulated value, you accept or reject your hypothesis, and can thereby conclude whether your data is significantly different or not.

Some of these steps have been covered in previous sections. If you need a refresher, just follow the appropriate link above. Others, such as hypotheses, one- and two-tailed tests, t-test and F-test, are described in this section.

Finally, at the end of this section, there is a flow-chart that describes the steps and options that you would go through when analyzing data. You may find this chart very useful as a visual reference for solving statistical and data analysis problems.

© Dr. David Stone (dstone at chem.utoronto.ca) & Jon Ellis (jon.ellis at utoronto.ca) , August 2006