Question

Huey and Dunham (1987) measured the running speed of fence lizards, Sceloporus merriam,in Big Bend National Park in Texas. Individual lizards were captured and placed in a 2.3-meter raceway, where their running speeds were measured. Lizards were then tagged and released. The data from the researchers is presented in modified form below. The lizard collections have occurred over three different years to see if the sprint speed of tagged lizards is changing over time.

Sprint Speed (m/s)

Lizard

Year One

Year Two

Year Three

1 1.43 1.37 1.60
2 1.56 1.30 1.71
3 1.64 1.36 1.83
4 2.13 1.54 1.92
5 1.96 1.82 1.09
6 1.89 1.79 2.06
7 1.72 1.72 1.86
8 1.80 1.80 1.78
9 1.87 1.87 2.04
10 1.61 1.88 2.13

The null hypothesis is that the mean of the lizard speed measurements are only different due to chance while the alternative hypothesis states that at least one year is different from the others.

[straight H subscript 0 : space straight mu subscript 1 equals space straight mu subscript 2 space equals space straight mu subscript 3 straight H subscript straight A : space at space least space one space straight mu subscript straight i space is space different space from space the space others]

Calculate the ANOVA table below.

Source of Variation Sum of Squares df Mean squares F-ratio [F subscript 0.05 left parenthesis 1 right parenthesis comma d f subscript g r o u p s end subscript comma d f subscript e r r o r end subscript end subscript]
Groups (treatments)
Error
Total

R2 =

Do the ANOVA results indicate that the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (HA)? (yes or no)

Answers should be rounded to the nearest three decimal places where appropriate

Answer 1

applying one way ANOVA:

R² = SSR / SST

= 0.133/1.807

=0.0734

Source of Variation SS df MS F P-value F0.05(2.27)

treatments 0.133 2 0.066 1.069 0.3574 3.354

error 1.675 27 0.062

Total 1.807 29

as p value is not significantly low:

Do the ANOVA results indicate that the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (HA)? -No

Explanation: