# worksheet for SSoriginal data (time to germination, daysAcidSandpaperAcid Sandpaper3538304931RazorRazor132515212715121614sumserrorGrand mean YdferrorMSerrorroupdfgroupsF-ratioMSgroups

Question
1. A conservation biologist is working on increasing population sizes of the silver-leaf lupine (Lupinus albifrons), which is the host plant for the endangered mission blue butterfly. Like many plants whose seeds have hard coats, germination in silver-leaf lupine is improved if the seedcoat is “scarified”—scratched or nicked before planting in order to help water penetrate to the embryo. The biologist tests time to germination associated with three different treatments: manual nicking with a razor blade (razor), a 30-minute acid bath in concentrated sulfuric acid (acid), and agitation between 2 pieces of sandpaper (sandpaper). Here are the data (time to germination of a seed, in days):

Razor: 15, 9, 12, 16, 14

Acid:  35, 38, 30, 49, 31

Sandpaper: 13, 25, 15, 21, 27
a) is this a fixed-effects or random-effects ANOVA? Explain how you know.

b) Fill in the ANOVA table below (you may write in by hand):

(ATTACHED)

c) What is the critical value of F for this experiment? Do you reject the null or not?

Step 1

Solution:

a) Effects of ANOVA:

It is given that three different treatments assigned to different seeds in three different ways.

The seeds across three different treatments are not same. Therefore, this is a random-effects ANOVA.

Step 2

b) Computation of ANOVA table:

From EXCEL, ANOVA table is obtained as follows:

• Select Data --> Data Analysis

Select Anova:Single factor from the Analysis tool and click ok.

Step 3

Calculation:

• Yi-bar is the sum of all the values in respective treatment divided by 5 and the grand mean is 33 by summing all 15 values divided by 15.
• Worksheet for SSerror has been calculated using the formula (yi−Yi-bar)^2. For the first cell, (15−13.2)2. Similarly, SSerror for other cells has been calculated.
• ni(Yi−Y-bar) for R...

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