Statistics For Science Fair Cheat Sheet (Page 2 of 2) in pdf

iv. Consider performing inference about the regression slope. This is a t-test with the null

hypothesis that there is no linear relationship. See section B (below) for more on t-tests.

v. Least squares regression and the correlation coefficient can only be used for data with a

linear relationship. If the relationship is not linear, more advanced methods can be used to

transform the relationship so least squares regression can be used.

b. Comparing data from two different groups. If your student is examining differences between two

groups of data, then an examination of boxplots and a t-test is probably the statistical path of

choice.

i. Plot the data using a side-by-side boxplot. Based on the plots, ask, “Does there appear to

be a difference between these groups?” “Does the experimental group seem to be larger or

smaller than the control group?”

ii. Based on the context of the project, determine the alternative hypothesis, H

. Do you think

that the experimental group has a smaller mean than the control group? That the

experimental group has a larger mean than the control group? Or simply that the groups are

different from one another?

iii. Define a level of significance (e.g. P< 0.05). Carry out the two-sample t-test, examine the P-

value, and determine if the difference between the groups is statistically significant.

iv. Evaluate the practical significance of the difference between the groups.

v. Report the results of the inferential analysis in the context of your experiment.

vi. If you are trying to determine if a set of data is different from a specific value, then the t-

procedures are probably still the statistical tool of choice. However, instead of using a two-

sample t-test, use a one-sample t-test. Also, if your student used a matched pairs design,

the t-procedures are slightly different; consult one of the references below for details.

vii. When comparing differences between more than two groups, ANOVA may be a more

appropriate choice. See one of the references below for details.

c. Inference for categorical variables. If a student is doing a genetics project, they are probably

interested in knowing whether the results of their experiment match the expected distribution of

phenotypes or genotypes. Other projects that have categorical variables that are expected to take a

specific distribution can also be analyzed with this technique.

i. Start with a two-way table. Calculate marginal distributions and determine the differences

between the marginal distributions of the experimental and control group(s).

ii. If possible, use a bar graph or pie chart to show the distribution differences among the

various groups. Remember that bar graphs are often easier to make and understand.

iii. Use a chi-square test for goodness of fit. Determine the test statistic, Χ

, and the p-value.

iv. If the chi-square test finds a significant result, examine the distribution to find the largest

components of the chi-square statistic.

4. We combine the results of exploratory data analysis and inferential analysis with our analytical

intuition to figure out what the data are telling us.

5. We clearly present our results using the language of statistics.

a. State the statistical hypothesis along with your scientific hypothesis in the hypothesis section of

your presentation/paper. Be sure to express the reasoning behind the hypothesis.

b. Use a flowchart to show the experimental design. In the methods/procedures section, point out how

replication, control, and randomization were utilized.

c. Show both exploratory data analysis and inferential analysis in the data analysis section. Discuss

the meaning of graphs and numerical measures. State the level of significance used in your tests

(e.g. P <0.05). State the conclusion of the significance test.

d. State the statistical and practical significance of the results in the conclusions section. Be sure to

state whether the null hypothesis was accepted or rejected.

Suggested References:

The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith, ISBN 9780062731029

Cliff Notes Quick Review: Statistics by David Voelker, Peter Orton, and Scott Adams, ISBN 9780764563881

The Practice of Statistics, 3

ed. by Daniel Yates, David Moore, and Daren Starnes, ISBN 9780716773092,

Statistics For Science Fair Cheat Sheet Page 2

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