Notes: September 2009

Monday, 28 September 2009

APPLE FOR APPLE

Rahul - Shalaka - Punam - Alex

Weights and heights are good examples of frequency distributions which "tend" to become bell - shaped (normal distribution) curves.

But try plotting these curves for

. A family of 10 persons

. 1000 people staying in same building

. Entire population of the world.

You will find that from an extremely SKEWED Curve (For family), you more to an extremely CENTRALIZED (bell - shape) curve, as you plot world's Population.

So, the first thing about these curves is SAMPLE SIZE or POPULATION.

In the enclosed graphs, our "Co - Professionals" populations (which we have plotted) are relatively" small. If these were one million in each case, we would have got a much smoother/ more centralized /less skewed curves.

Then again, 1000 people staying in same building. Surely that curve looks better than the curve for 10 family members. Now you can make it look even better if you plot a curve for height or weight of only those people (amongst those 1000) who are

. Of same "age" (say 10 years)

It will further improve if you plot

. Only "Girls" of 10 years of age.

So, besides sample - size (population), the smoothness / centralization of a curve has a lot to do with

"Similarities amongst the member of the population"
i.e. "Apple - For - Apple" comparison Unfortunately, our "Populations" contain lots of "Dis - similar" persons !

eg. "Banking/ Insurance" Professionals

. Your population was 100,000 people and

. You plotted a "Sub - population" of

- Same Age

- Same Experiences (yrs)

- Same DEGREE

- Same Sub - Sector (Pvt. Vs. Public)

- Same Region etc.

Then you are bound to get a much smoother / centralized distribution where "extremes" of Raw - Scores have very low probability of occurrence. Given this (theoretical) background, it will take a very long time for our graphs to become NORMAL / BELL - shaped, when populations of each type of "Co - professional's reach 100,000 or more.

Till then the graphs will look terrible at least to people who do not have much exposure to statistics. It may even lead to disbelief / skepticism/ rejection of the very concept !

We cannot afford this.

May be "Cumu. Percentage Vs. Raw Score" chart drawn by you in enclosed page is our answer.

It is simple to understand (institute), which makes it ELEGANT.

No "Mean"

No "Standard Deviation (6)"

No Skew (to confuse)

Just one vertical and one horizontal drop are sufficient to tell the candidate.

. What is my Score? (Raw Score)

. Where do I stand ? (Percentile Score)

Amongst my Co - profs

. How many Co - profs. ? (Population)

This graph is not "Cluttered - Up" with several lines or tabulations showing population between +10 & -10 (- which, in any case, a candidate does not understand !)

I believe because of the concept of "Comu. Percentage of Co - professionals. Vs "Raw Scroe",

The graphs (for any function / skill / any population - size / any combination of age / exp/ education level /region etc)

Will always come out as shown by you.

It will always (or almost always) be a smooth, upward curve without "Kinks" - especially, if your RAW - SCROE DATA TABLE, increases raw - scores by 1, i.e. 1, 2, 3, 4, 5 ......... 100

I suppose Microsoft Chart, will automatically adjust the X axis and automatically restrict it when "Percentile - Score" figure hits 100. Y axis will always remain as shown by you.

Suggest you / shalaka quickly experiment with 10/15 other FUNCTION - SKILL populations to assure us that this concept will always work, and that we are able to programmatically generate / drop the horizontal / vertical lines as shown in enclosed sample graph.

You may want to adopt this concept also for "SALARY GRAPH" (makes sense), what about TENURE GRAPH ?

I believe, this SIMPLIFICATION (-and avoidance of statistical jargon) will attract the candidates.

Hemen Parekh