How to do hypothesis testing for two different counts?

Amazonian 04/06/2018. 2 answers, 53 views
hypothesis-testing inference poisson-distribution count-data z-test

I have the following problem: in year A, we observe that a company sold N_A of its product, in year B, we observe that the company sold N_B of its products. How do I do hypothesis testing that the company sold statistically different number of products in year A and B?

My thought is that

     N_A ~ Poisson(lambda_A)
     N_B ~ Poisson(lambda_B)

So my hypothesis test is

     H_0: lambda_A = lambda_B
     H_1: lambda_A != lambda_B

Then I can run a z-test where the test statistic

     Z = |N_A - N_B|/sqrt(N_A + N_B)

follows a normal distribution with mean 0 and variance 1.

Is this the correct method? If so, why can the Z-test be applied in this case?

2 Answers


Eric Mittman 04/06/2018.

By using the Poisson distribution, we get that the "noise" in the measurements is proportional to the square root of the expected value. This is a pretty major assumption.

The expected value of the difference of two i.i.d. random variables are zero and the variance of the difference is twice the variance of one of them.

Further, if we assume that the distribution of the difference is approximately normal -- which seems reasonable for large Poisson counts -- we end up with this z-statistic.


SmallChess 04/06/2018.

Statistical testing is meaningless here as you have no measure of variability. All you have is just two data points, one for company A and for company B.


HighResolutionMusic.com - Download Hi-Res Songs

1 (G)I-DLE

POP/STARS flac

(G)I-DLE. 2018. Writer: Riot Music Team;Harloe.
2 The Chainsmokers

Beach House flac

The Chainsmokers. 2018. Writer: Andrew Taggart.
3 Ariana Grande

​Thank U, Next flac

Ariana Grande. 2018. Writer: Crazy Mike;Scootie;Victoria Monét;Tayla Parx;TBHits;Ariana Grande.
4 Nicki Minaj

No Candle No Light flac

Nicki Minaj. 2018. Writer: Denisia “Blu June” Andrews;Kathryn Ostenberg;Brittany "Chi" Coney;Brian Lee;TJ Routon;Tushar Apte;ZAYN;Nicki Minaj.
5 Clean Bandit

Baby flac

Clean Bandit. 2018. Writer: Jack Patterson;Kamille;Jason Evigan;Matthew Knott;Marina;Luis Fonsi.
6 Imagine Dragons

Bad Liar flac

Imagine Dragons. 2018. Writer: Jorgen Odegard;Daniel Platzman;Ben McKee;Wayne Sermon;Aja Volkman;Dan Reynolds.
7 Halsey

Without Me flac

Halsey. 2018. Writer: Halsey;Delacey;Louis Bell;Amy Allen;Justin Timberlake;Timbaland;Scott Storch.
8 BTS

Waste It On Me flac

BTS. 2018. Writer: Steve Aoki;Jeff Halavacs;Ryan Ogren;Michael Gazzo;Nate Cyphert;Sean Foreman;RM.
9 BlackPink

Kiss And Make Up flac

BlackPink. 2018. Writer: Soke;Kny Factory;Billboard;Chelcee Grimes;Teddy Park;Marc Vincent;Dua Lipa.
10 Fitz And The Tantrums

HandClap flac

Fitz And The Tantrums. 2017. Writer: Fitz And The Tantrums;Eric Frederic;Sam Hollander.
11 Backstreet Boys

Chances flac

Backstreet Boys. 2018.
12 Kelly Clarkson

Never Enough flac

Kelly Clarkson. 2018. Writer: Benj Pasek;Justin Paul.
13 Diplo

Close To Me flac

Diplo. 2018. Writer: Ellie Goulding;Savan Kotecha;Peter Svensson;Ilya;Swae Lee;Diplo.
14 Anne-Marie

Rewrite The Stars flac

Anne-Marie. 2018. Writer: Benj Pasek;Justin Paul.
15 Little Mix

Woman Like Me flac

Little Mix. 2018. Writer: Nicki Minaj;Steve Mac;Ed Sheeran;Jess Glynne.
16 Imagine Dragons

Machine flac

Imagine Dragons. 2018. Writer: Wayne Sermon;Daniel Platzman;Dan Reynolds;Ben McKee;Alex Da Kid.
17 Little Mix

The Cure flac

Little Mix. 2018.
18 Bradley Cooper

Always Remember Us This Way flac

Bradley Cooper. 2018. Writer: Lady Gaga;Dave Cobb.
19 Rita Ora

Velvet Rope flac

Rita Ora. 2018.
20 Lady Gaga

I'll Never Love Again flac

Lady Gaga. 2018. Writer: Benjamin Rice;Lady Gaga.

Related questions

Hot questions

Language

Popular Tags