Chi-Square Analysis

• Use statistics to determine if the difference in data obtained vs. expected is due to random variation or another mechanism
• Smaller the chi-square value = difference is due to randomness in the system

Null Hypothesis

• A null hypothesis states:
  • There is NO substantial statistical difference between observed values and the expected values (of flipping one coin 20 times)
  • The differences between observed and expected data are totally random, by chance alone

Chi-Square Set-Up

• Calculate the expected number in each outcome (“E”)
• Determine the number observed for each outcome (“O”)
• Do this for every data set
  • Ex: Flipping a coin 40 times

DF Value

• DEGREES OF FREEDOM (DF): the number of possible grouping of results in the experiment minus one
  • DF = # of result groups – 1
  • DF = 2 (heads/tails) – 1 = 1
• Now determine if the null hypothesis is supported or rejected using the Chi-Square table

Chi Square Value

• If the null hypothesis is supported…

  • Assumption = event is random, and no other mechanism played a role in the experiment and vice-versa

  • Each flip of a coin is completely random with an equal chance of either heads or tails landing up

    Example: Each flip of a coin is completely random wit an equal chance of either heads or tails landing up

How To Write Your Results:

• Use the following formula sentence:
  • With _____ degrees of freedom, my chi square value is _____, which gives me a p value between ____% and ____%, I therefore _____ (accept/reject) my null hypothesis
• Use this sentence for your results sections of a lab
• Your explanation of what the significance of this data means is your conclusion