EXPERIMENTAL DESIGNS AND DATA ANALYSIS

The focus of this site is on experimental design, the methods used for data

collection, and analysis.

 

The goal in the chemistry laboratory is to obtain reliable results while realizing there are errors inherent in any laboratory technique.  Some laboratory errors are more obvious than others.  Replication of a particular experiment allows an analysis of the reproducibility (precision) of a measurement, while using different methods to perform the same measurement allows a gauge of the truth of the data (accuracy).

 

There are two types of experimental error:  systematic and random error.

 

Systematic error results in a flaw in experimental design or equipment and can be detected and corrected.  For example if your equipment is not calibrated to zero; this can be fixed.  You should control this type of error by periodically checking the scale throughout the experiment to ensure that calibration doesn’t degrade over time.  This type of error leads to inaccurate measurements of the true value. 

 

On the other hand, random error is always present and cannot be corrected.  Random error is inherent in measurement.   An example of random error is that of reading a burette, which is somewhat subjective and therefore varies with the person making the reading.  Sometimes even the same sample could yield different measurements on the same instrument!

 

This type of error impacts the precision or reproducibility of the measurement. 

 

The goal in a chemistry experiment is to eliminate systematic error and minimize random error to obtain a high degree of both accuracy and precision.

 

Expression of experimental results is best done after replicate trials that report the average of the measurements (the mean) and the size of the uncertainty, the standard deviation.  Both are easily calculated in such programs as Excel.  The standard deviation of the trial reflects the precision of the measurements.  Whenever possible you should provide a quantitative estimate of the precision of your measurements.  The accuracy is often reported by calculating the experimental error.

 

You should then reflect upon and discuss possible sources for random error in your measurements that contribute to the observed random error.  Sources of random error will vary depending on the specific experimental techniques used.  Some examples might include reading a burette, the error tolerances for an electronic balance etc.  Sources of random error do NOT include calculation error (a systematic error that can be corrected), mistakes in making solutions (also a systematic error), or your lab partner (who might be saying the same thing about you!)

Basic principles

Three basic principles necessary to provide valid and efficient control of experimental error should be followed in the design and layout of experiments. These are:

Replication - Replication provides an estimate of experimental error; improves the precision of the experiment by reducing standard error of the mean, and increases the scope of inference of the experimental results.   If you replicate the results, one time they may come out high and the next time low, then find the mean, and error may be minimized.

Although if for example you are massing individual pennies 20 times, and each measurement is above the true value, and then you are using that data in a multiplication calculation, the error is propagated.  Meaning, you are multiplying the error too (not good.)

Randomization. This is practiced to avoid bias in the estimate of experimental error and to ensure the validity of the statistical tests.  This means that your sample should be as random as possible.  You shouldn’t select your sample.

Sample size - The recommended sample size for each experiment should be as large as possible while still manageable. The larger the sample size the less the impact of individual differences.  A lower sample size could be used for multiple trials, but maintaining the same number in each trial is advantageous.  Using an unequal sampling, then averaging would lead to a weighted error in the direction of the smaller sample. 

Error Reduction

Consider the following questions.

 

Averaging

Random assignment means that each subject has an equal chance (probability) to be assigned to a control or experimental group.

 

MEASUREMENT

A flawless design will be invalidated by an inappropriate measuring instrument.

DATA COLLECTION, ORGANIZATION AND DISPLAY

INTRODUCTION

The purpose of experimentation or observation is to collect data to test the hypothesis.

 Information should include, but is not limited to,

DATA TABLES

The "best" tables provide the most information in the least confusing manner.

DRAWING CONCLUSIONS

INTRODUCTION

The conclusion should contain the following sections:

 discuss the "significance" (value) and/or implications of the research.

Questions to be considered might include the following:

 

SUPPORTING CONCLUSIONS

 

More on Making comparisons

When making comparisons ...

MAKING PREDICTIONS

One of the strongest supports for a cause and effect relationship is to be able to predict the effects of the independent variable on the dependent variable.

EXPLAINING DISCREPANCIES

 

Flaws in the experimental design should be pointed out with suggestions for their elimination or reduction.

Questions to be considered might be...

discuss any discrepancies in the data or its analysis.

EXPERIMENTAL ERROR AND ITS CONTROL

LIMITATIONS OF A STUDY

do not generalizing the results to an entire population... Limit the conclusions to what was tested.

"in vitro" (in the laboratory) may not produce the same results as those done "in situ" (under natural conditions). It is not always possible to control the interactions of variables under natural conditions.

Synergistic effects occur when variables interact.

These may modify or create entirely new effects that neither variable would produce if tested alone.

Do not propose assumptions that can not be supported.

Avoid editorializing.

EXPRESSING MEASUREMENT

 Rules for the written expression of SI units are as follow:

Capitalization:

Plurals:

Punctuation:

 

SIGNIFICANT DIGITS

Rules to determine significant digits.

1.    Digits other than zero are always significant.... 23.45 ml (4) 0.43 g (2) 69991 km (5)

2.    One or more final zeros used after the decimal point....8.600 mg (4) 29.0 cm (3) 0.1390 g (4)

3.    Zeros between two other significant digits....10025 mm (5) 3.09 cl (3) 0.704 dc (3)

4.    Zeros used for spacing the decimal point or place holding are not significant....5000 m (1) 0.0001 ml (1) 0.01020 (4)

 

 Rules for determining significant digits when calculations are involved.

An answer can not be any more accurate than the value with the least number of significant digits.

1.    Addition and Subtraction - after making the computation the answer is rounded off to the decimal place of the least accurate digit in the problem.

2.    Multiplication and Division - after making the computation the answer should have the same number of significant digits as the term with the least number of significant digits in the problem.

When using calculators…

 

SCIENTIFIC NOTATION

 

Examples of scientific notation.

1.    Avogadro's Number = 602 217 000 000 000 000 000 000 molecules = 6.02217 X 1023 molecules

2.    Angstrom = 0.000 000 000 1 m = 1 x 10-9 m

 

Calculations with Scientific Notation

Calculator rounding

 ACCURACY IN MEASUREMENT

Accuracy refers to how close a measurement is to the accepted value. It may be expressed in terms of absolute or relative error.

Absolute error is the difference between an observed (measured) value and the accepted value of a physical quantity. In the laboratory it is often referred to as experimental error.

Absolute Error = Observed-Accepted

Relative error is a ratio of the absolute error compared to the accepted value and expressed as a percent. It is generally called the percent of error.

The accuracy of a measurement can only be determined if the accepted value of the measurement is known.

PRECISION IN MEASUREMENT

Precision relates to the uncertainty (+ or -) in a set of measurements. It is an agreement between the numerical values of a set of measurements taken in the same way. It is expressed as absolute or relative deviation.

Uncertainty example 1

EXAMPLE 1:

The value read on the triple beam balance is 2.35 grams. This triple beam balance has an accuracy (absolute uncertainty) of plus or minus 0.1 gram. Because this balance can not measure values less than 0.1 gram, the last digit in 2.35 grams is referred to as being doubtful. That is to say we are uncertain as to the accuracy. It could be 2.36 grams, or 2.34 grams, or even 2.33 grams. While the number of significant digits is three the last number is doubtful. We are uncertain of its exact value because our measuring device only has an accuracy of 0.1 gram.

 READING INSTRUMENTS

 

Calibrating Instruments

 MEASURES OF CENTRAL TENDENCY

Arithmetic Mean

Mode

 

SYMMETRY

 

Skewed Frequency Curves