Chi-Square Test How do you know if your data is the result of - - PowerPoint PPT Presentation

Chi-Square Test

How do you know if your data is the result of random chance or environmental variables?

Chi-Square Test

• Used to compare categorical data and

evaluate if differences between the data sets are statistically significant or due to chance In other words…

• Is the variation between observed and

expected data due to chance or due to other factors (variables)?

Chi-square Sum Observed values Expected values

Null Hypothesis (H0)

• States that there is no statistical significant

difference between the observed and expected frequencies

• In statistics, a “significant” difference means

there is a less than 5% chance that the variation in the data is due to random/chance events

• Goal of an experiment is to invalidate (or

“nullify”) the null hypothesis

Effect of Fertilizer on Plant Growth

Null Hypothesis (H0) The application of fertilizer does not affect plant growth. Alternative Hypothesis (H1) The application of fertilizer affects plant growth.

Effect of Humidity on Isopod Behavior

Null Hypothesis (H0) Alternative Hypothesis (H1)

Effect of Humidity on Isopod Behavior

Expected Values? Observed Values?

Application of the Chi-Square Test

• Used to either fail to reject or reject the null

hypothesis

• Fail to reject? The variation in the data is due

to chance (bad data!)

• Reject? The variation in the data is due to

some variable in the experiment (good data!)

Is the difference between observed and expected values due to chance or a variable?

• Expect?
• Observed = 57 brown, 43 white
• B (brown)
• b (white)
• 100 plants

How to Use the Chi-Square Test

• 1st – Specify the null hypothesis
• 2nd – Determine the degrees of freedom (n-1)

(number of possible outcomes – 1)

• 3rd – Determine the critical value using Chi-

Square Distribution Table (p = 0.05, or 95% sure)

• 4th – Calculate Chi-Square
• 5th – Compare Chi-Square value with the

critical value

Degrees of Freedom

Degrees of Freedom

Determine Critical Value

• Is your chi-square value in the RED zone?

Then you CANNOT claim that the variation in the data observed is due to the variable you are testing

Not Significant Significant

Chi-Square Value?

• If the chi-squared value exceeds (or is greater

than) the critical value, then you reject the null hypothesis. This means that the variation in the data is due to a variable being tested (“statistically significant”).

• If the chi-squared value is less than the critical

value, then you fail to reject the null

• hypothesis. This means that the variation in

the data is due to chance.

Calculate Chi-Square for Activity A2