Test for Significant Differences

T- Tests

T- Test

• T-test – is a statistical test that compares two data sets, and determines if there is a significant difference between two data sets.

T- Test

Calculating T-Test

• To calculate a test test (t-values) you need the following information: – Mean– Standard deviation– Sample size

You don’t need to calculate t-values – excel will do it for you.

T-Tables

• Degrees of freedom (df): Sum of sample sizes minus 2

• Probability Values (p-value) – Probably that the difference occurred by chance alone

Degrees of Freedom

• What is our sample size?• 20• What is the degrees of

freedom?• 20 – 2 =18

Boys Scores

Girls Scores

1 60 98

2 62 42

3 68 88

4 70 92

5 63 38

6 65 56

7 65 95

8 58 92

9 64 50

10 63 89

What does it all mean?

• If your sample size is 10 and your t-value is 5.00, what is your probably (p-value) that the difference between two sets occurred by chance?

• Degrees of freedom (df) = 8• P-value is 0.001 which means there is a 0.1% chance that the

difference occurred by chance. Thus the difference between the two data sets is probably statistically significant.

Null Hypothesis H0

Significant Differences

• If you carry out a statistical significance test, such as the t-test, the result is a P value, where P is the probability that there is no difference between the two samples. – A. When there is no difference between the two

samples:• A small difference in the results gives a higher P value, which

suggests that there is no true difference between the two samples

• By convention, if P > 0.05 you can conclude that the result is not significant (the two samples are not significantly different).

Significant Differences

• If you carry out a statistical significance test, such as the t-test, the result is a P value, where P is the probability that there is no difference between the two samples.

• B. When there is a difference between the two samples:– A larger difference in results gives a lower P value, which makes

you suspect there is a true difference (assuming you have a good sample size).

– By convention, if P < 0.05 you say the result is statistically significant.

– If P < 0.01 you say the result is highly significant and you can be more confident you have found a true effect.

P-Value Summary

P-value & Null Hypothesis

• In biology the critical probability (P-value) is usually taken as 0.05 (or 5%). This may seem very low, but it reflects the facts that biology experiments are expected to produce quite varied results.

• If P > 5% then the two sets are the same (i.e. accept the null hypothesis).– Null hypothesis is always A PREDICTION stating that there is no

significant differences between data sets.• If P < 5% then the two sets are different (i.e. reject the null

hypothesis). – Null hypothesis is always A PREDICTION stating that there is no

significant differences between data sets.

T-Test & Excel

T-Test & Excel

T-Test & Excel

Your turn.Day 2 Run a T-test comparing the data sets to test to see if you have a significant difference between snail shells in habitats with and without crabs. .• Screen shot you excel calculations and

insert them into a word document. • In an organized table report your p-value, t-

value, degrees of freedom.• State your null hypothesis.• State whether you accept of reject your

null hypothesis.• Provide a reason for your statement in d.

Your reason should include your p-values.• Provide a scientific reason for your results.