t-test hypothesis tests: The mean/median of Group A = the mean/median of Group B
One-way ANOVA hypothesis tests: 3 groups. Tests means/medians of A = B = C
Descriptive Statistics: (e.g., mean, s.d., SEM, etc.) help organize/summarize data
Inferential Statistics: (e.g., t-test and ANOVA) allows us to generalize conclusions
Both are experimental studies, both have ind. & dep. variables, subtle difference
Variable - "characteristic that may differ from one biological entity to another" Zar (2010)
All experiments have at least 1 of each
How many variables & data type and scale of measurement dictate which inferential tool to apply
Prairie lizard manipulative study
Dep. - Snout vent length
Ind. Temperature at
Other factors (nuisance/confounding variables)
Approaches to nuisance/confounding variables
If concerned about "Procedural Effects": Implement a Control(s)
Examples of variable types and their scales of measurement
Continuous in cm --> Ordinal in ranks
What is a "low" P-value?
Insert probability notes here
Family-wise error inflation is when doing multiple comparisons with the same data at the same alpha level. Raises Type I error rate
H0: u1 = u2 = u3 ...
Sum of squared deviations within each group. Usually obtained by subtraction
Having calculated MSgroup and MSerror we can now calculate F
Between groups estimate of the population variance is much larger than the within groups estimate ® F value greater than 1
How much larger than 1.0 must the value of F be to decide that there are differences among the means?
Use tables of the F distribution, Zar Table B4, Appendix 21.
Gives critical values of F corresponding to the degrees of freedom for the two mean squares (dfgroup and dferror).
dfgroup = numerator df (2)
dferror = denominator df (12)
From tables: (alpha = 0.05) Fcrit=5.10 (F2,12 = 8.45)
Because Fobt > Fcrit we can reject Ho and conclude that the groups were sampled from populations with different means. There is an effect of Sandwich Type
Factorial Analysis of Variance
2x2 Design Rat & Lard Example