Question

A scientist is interested in whether the color of rice (white vs. brown) makes birds explode with greater force. Six pigeons were captured in Liberty Park. Each was then force-fed five pounds of rice, and the power of the ensuing explosion was then measured: Explosion Strength Rice in Megatons

White 2 White 2 White 3 Brown 8 Brown 9 Brown 10

Perform the one way ANOVA. What’s the between sum of squares (BSS)?

Answer 1

Let's perform the one-way ANOVA test to check whether there is a difference in the power between the two groups.

Ho: B1 = B2 = 0

Ha: There is a significant difference between the two groups

Let's find the SS_bet:

Here, i are the groups, i = 1 and 2

x-bar = Grand mean = 5.67

Group 1 mean = 2.33

Group 2 mean = 9

SS_b = 3*(5.67 - 2.33)² + 3*(5.67 - 9)²

= 66.67

Let's find SSE:

Si is the standard deviation of group i

S1 = 0.577, S2 = 1

SSE = 2*0.577² + 2*1² = 2.67

The table can be formed as below:

Source	DF	Sum of Square	Mean Square	F Statistic	P-value
Groups (between groups)	p - 1 = 2 - 1 = 1	66.666673	66.666673	100.000033	0.000562003
Error (within groups)	n - p = 6 - 2 = 4	2.666666	0.666667
Total	5	69.333339	13.866668

The F-statistic = 100.00

The p-value at df = 1 and 4 is 0.00056

As the p-value < 0.05, we can reject the null hypothesis. Hence, we conclude that we have enough evidence to say that there is a significant difference in the power of the ensuing explosion between the two groups.