Question

Use a one-way ANOVA test to study the price difference between cruelty-free products and those tested on animals

• Select at least seven different products for your one-way ANOVA test: for example, you may select laundry detergent or mascara. Share your results.
• Are there significant price differences?
• Explain whether or not there are other factors to consider in the price differences between your selected products.

Answer 1

Products	Cruelty free	Tested on animals
Foundation	39	43
Concealer	29	28
Lipstick	19	22
Serum	54	41
Perfume mist	12	13.07
Body oil	26	32
Soap	12	15

These are a few products from well known brands and can be found easily online.

Null hypo: There is no significance difference between animal tested and cruelty free products prices.

VS

Alternative hypo: There is significance difference between animal tested and cruelty free products prices.

We will conduct the test at 0.05 level of significance.

ANOVA
Source of Variation	SS	df	MS (SS/df)	F (SSb/ SSr)	P-value (P > F)	F crit
Between Groups	0.673207	1 (k - 1)	0.673207	0.003625	0.953	4.75
Within Groups	2228.801	12 (n - k)	185.7334
Total	2229.475	13

As you can see that p-value > 0.05 and also Test stat (F) < critical (F crit )

WE don't reject the null hypothesis and conclude that there is no significant difference between cruelty free and animal tested product prices at 0.05 level of significance.

This is ANOVA - Single Factor. We first need to find the and . They are 'Total variance' and 'Variance in between the treatments' respectively.

We know

=

Grand total = 385.07 Sum of individual squares = 12820.82

= 2229.48

=

Note: We have to separately sum for all the treatment.

=

= 10592.7

=0.673

2228.80

We can also use excel data analysis function

Steps:

1. Input data
2. Click on 'Data' on toolbar and then click on data analysis
3. Select 'Anova- Single Factor'
4. Input your range and other info accordingly and you will get your analysis