Small Sample Size - Test for Difference between Brands with Normal Distribution

[HeapofAsh]

Lets say I have 8 samples (weight) of 4 ingredients in particular food by X brand and another 8 samples by Y brand. I would like to test to see if there is any difference between the two brands in terms of weight of particular ingredients. However, I am not sure what statistic test to run and I don't know whether my data is normal or not (especially because my sample size is small). Any guidance will be helpful.

Thnx

 

[Ray Vickson]

Lets say I have 8 samples (weight) of 4 ingredients in particular food by X brand and another 8 samples by Y brand. I would like to test to see if there is any difference between the two brands in terms of weight of particular ingredients. However, I am not sure what statistic test to run and I don't know whether my data is normal or not (especially because my sample size is small). Any guidance will be helpful.

Thnx

If you are able to assume that the data are at least approximately normally distributed, this would be a two-way analysis-of-variance problem (ANOVA), where you have two brands (X and Y) along one "axis" and ingredient type (1,2,3,4) along the other "axis". WARNING: this is an example of a so-called "nested" two-way ANOVA, because we do not 'cross' ingredient with brand (which would give 4x2 = 8 combinations repeated 8 times---for a total of 8x8 = 64 data points), but rather, just 16 data points. To see what type of tests to perform, look up 'Nested ANOVA'.

You should be aware that some of this type of material is often only covered in a second course in Applied Statistics, and that students have trouble grasping some of it---not to mention getting terminally confused and making lots of errors. Looking at a book (rather than a web page) is preferable, but it should probably not be an introductory textbook.

Anyway, for what it is worth, see, eg.,
http://www.stat.purdue.edu/~zhanghao/STAT514/handout/nested.pdf
http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc233.htm
http://biol09.biol.umontreal.ca/PLcourses/Nested_and_two-way_anova.pdf
http://www3.imperial.ac.uk/pls/portallive/docs/1/1171923.PDF

Other issues arise if the data are not normally distributed (or at least, approximately so), and I know little to nothing about how to proceed in that case. Look up 'non-parametric methods'.

 

[HeapofAsh]

You should be aware that some of this type of material is often only covered in a second course in Applied Statistics, and that students have trouble grasping some of it---not to mention getting terminally confused and making lots of errors. Looking at a book (rather than a web page) is preferable, but it should probably not be an introductory textbook.

Yeah it seems beyond my stat course level. How about doing hypothesis test on difference of means or proportion of each type of ingredient.

For the amount (weight) of flour in food by Brand x and Brand y:
H₀:P_x= P_y
H_A:P_x≠ P_y

And do the same for different ingredients. If they it turns out that the P_x= P_y for all 4 different ingredients, would i be able to say there are no significant difference between the two brands (at least in terms of amount of ingredients).