Error & Statistical Analysis

Mini Lesson Unit 2 Types of Errors

Random Errors Random errors are statistical fluctuations (in either direction) in the measured data due to the precision limitations of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly the same way to get exactly the same number.

How to Minimize Random Errors? Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations.

Systematic Errors Systematic errors, by contrast, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are often due to a problem which persists throughout the entire experiment.

How to Minimize Systematic Errors Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is off in the same direction (either too high or too low). Spotting and correcting for systematic error takes a lot of care.

The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared ) in the experiment. What kind of error is this? 1.A random error 2.A systematic error 3.A stupid error 4.A partial error

You measure a ring 3 times and your measurements are: g,17.15g and 17.08g This is a result of a… 1.A random error 2.A systematic error 3.A stupid error 4.A partial error

Statistical Analysis

Statistics Statistics are a way to test that any differences in your data are a result of the variables you are testing and not a result of random chance. There are different statistical tests that you can run. The test you need depends on the type of data that you collected.

Null Hypothesis Null hypothesis: This is a statement that is the antithesis (opposite) of the hypothesis you are testing in your experiment. This hypothesis assumes there is no difference in the data.

Confidence Interval Confidence interval: This is the amount of certainty that you are willing to accept in your experiment. For our purposes this should be set at 95%. In other words you want to be 95% sure that the difference in your data is caused by the variable you tested and only 5% sure that the differences are due to random errors.

p-values –The results of your statistical test will generate a p-value (others are possible but this are the 2 most common). Your p-value should be compared to the amount of error you set at the beginning of the experiment. For our purposes this means 5% or –If the p-value is <= 0.05, the null hypothesis is rejected (the differences in the data are due to the tested variables).

ANalysis Of Variance (ANOVA) Use this test to compare the mean values (averages) of more than two sets of data where there is more than one independent variable but only one dependent variable. If you find that your data differ significantly, this says only that at least two of the data sets differ from one another, not that all of your tested data sets differ from one another. If your ANOVA test indicates that there is a statistical difference in your data, you should also run a t-test to see which independent variables produce significantly different results. This test essentially penalizes you more and more as you add more and more independent variables, making it more difficult to reject the null hypothesis than if you had tested fewer independent variables.

t-test The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups

Things that I am looking for in your lab notebooks… Title, date, group members, purpose Pre-lab questions (answered) Procedure parts: –Research question, alternative hypothesis, null hypothesis –Data table –ANOVA results –T-Test results –Reporting your results Summary

Data Table Trials# Skittles# Plain M&Ms# Peanut M&Ms AVG.