Experimental Designs and Data Analysis

EXPERIMENTAL DESIGNS AND DATA ANALYSISEXPERIMENTAL DESIGNS AND DATA ANALYSIS

The focus 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. 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. An example of random error is that of reading a burette, which is somewhat subjective and therefore varies with the person making the reading. Another random error may be when the sample or subjects vary slightly. These types of error impact 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 of Error

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, and then find the mean, error may be minimized.

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.

· The design of an experiment is the most critical part of any research.

· Even the very best data analysis is rendered useless by a flawed design.

· There are three areas to consider during your design.

Percent Error (Percent Deviation, Relative Error) and Accuracy

When scientists need to compare the results of two different measurements, the absolute difference between the values is of very little use. The magnitude of error of being off by 10 cm depends on whether you are measuring the length of a piece of paper or the distance from New Orleans to Houston. To express the magnitude of the error (or deviation) between two measurements scientists invariably use percent error.

If you are comparing your value to an accepted value, you first subtract the two values so that the difference you get is a positive number. This is called taking the absolute value of the difference. Then you divide this result (the difference) by the accepted value to get a fraction, and then multiply by 100% to get the percent error.

So, % error = | your result - accepted value | x 100%
accepted value

Several points should be noted when using this equation to obtain a percent error.

1) When you subtract note how many significant figures remain after the subtraction, and
express your final answer to no more than that number of digits.

2) Treat the % symbol as a unit. The fraction is dimensionless because units
in the values will cancel.

3) Notice that the error is a positive number if the experimental value is high, and is a negative number if the experimental value is low.

4) Usually you can minimize the margin of error by using a larger sample size.

5) The margin (size) of error depends on what you are measuring. If you are measuring the length of a room and have an error of 1cm, the error is minimal compared to measuring a worm and having a 1cm error. The error is larger even though it is 1cm in both cases.

Example of % error: A student measures the volume of a 2.50 liter container to be 2.38 liters.
What is the percent error in the student's measurement?

%error = = (accepted value – experimental value) x 100%
accepted value

Ans. % error = (2.50 liters - 2.38 liters) x 100%
2.50 liters

= (.12 liters) x 100%
2.50 liters

= .048 x 100%

= 4.8% error

Error Reduction

Consider the following questions.

· were the control and/or experimental groups equal before the beginning of the experiment

· How are individual differences controlled

· What was done to control for selection bias?

· How appropriate is the measuring device employed?

Averaging to reduce error

· The effects of unusual values (observations) can be reduced by taking an average.

· This average is referred to as the arithmetic mean.

· In general, the larger the sample size the more chance mean is correct.

· In experimentation where there are no groups averaging, it is accomplished by conducting numerous trials. But this would be a problem if this design were used alone if your instrument is reading high because all your trials would be high.

· Error is generally reduced through averaging averages. It’s true a larger sample would give a better average, but if there’s only one lab doing the experiment they can’t feasibly use 2000 items for their sample. Then it would be better to do the experiment 4 times with samples of 50 each time and average that data.

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

· Best accomplished by trusting a computer program that picks random numbers without replacement.

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.

· Data is a plural noun and datum is its singular form.

· Data refers to things that are known, observed, or assumed.

· Based on the facts and figures collected during an experiment, conclusions about the hypothesis can be inferred.

· data include stables, graphs, illustrations, photographs and journals.

Information should include, but is not limited to,

· step-by-step procedures,

· quantities used,

· formulas,

· equations,

· quantitative and qualitative observations,

· material lists,

· references,

· special instructions,

· diagrams,

· procedures,

· data tables,

· flow charts

DATA TABLES

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

· contain qualitative or quantitative observations.

· Qualitative data is descriptive but contains no measurements. Quantitative data is also descriptive but is based on measurements.

· titled and preceded with consecutive identification references such as "Figure 1, Figure 2"

· labeled columns.

· quantity labels in the column headers and not the columns themselves.

· consistent significant digits

DRAWING CONCLUSIONS

INTRODUCTION

The conclusion should contain the following sections:

· A restatement of the problem, purpose, or hypothesis.

· A rejection or failure to reject the hypothesis.

· Rational (support) for the decision on the hypothesis

· Discussion on the significance (value) and implications regarding the experiment.

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

Questions to be considered might include the following:

· Why was the research conducted?

· Of what practical value is the research?

· How could the results be applied to a "real" situation or problem?

· What implications could this research have on solving future problems?

· Can the results be used to predict future events and if so how accurately?

· What can be inferred about the total population, based on the analysis of the sample population?

· Did the research suggest other avenues for further investigations?

SUPPORTING CONCLUSIONS

· Be sure to refer to the data in explaining how the conclusion was drawn.

· Make direct references to the appropriate illustrations, tables, and graphs.

· Make comparisons among the control and experimental groups.

· Each comparison should have a paragraph of its own.

· Point out similarities and differences.