A Web-survey on Donation funded education model

A few days back I conducted a small survey on donation funded education model using LinkedIn, Facebook and some WhatsApp groups using the SurveyMonkey tool. I would estimate the total number of unique individuals reached by these groups would be at least 7500. I obtained 64 responses which is less than 1% of the total possible. However, the sample size is in itself not as big a problem as is the lack of knowledge whether it is a random sample from the population. We often talk of this in basic statistics courses but many forget about this "Caution" in practice.

In traditional statistics the big assumptions regarding sample collection are: (i) the sample is a "probability sample" with each individual having a "known" probability (not necessarily equal) of being selected in the population, (ii) the sample size is fixed in advance,  (iii) there is no non-response i.e. everyone who is selected for inclusion in the survey answers the survey and (iv) the respondents answer the survey question truthfully. In case of my survey, unfortunately, none of these assumptions hold true.

Why these four assumptions are important? The main purpose of having the above four assumptions is to ensure generalisability of the results. The results of a survey in which the above assumptions do not hold true cannot be generalised to the entire population. However it may give useful insights which can be verified by a well-controlled study later on.

What insights did I get from my survey? Remember these are merely indications and correctness of these would depend upon the extent to which the assumptions (i)-(iv) are violated (which we can never know).

1. About 66% of the respondents found Higher education in India "Expensive" or "Very Expensive" with 12% of the respondents finding it to be "Very Expensive"

2. About 42% of the respondents felt that availability of education loans does NOT justify the very high fees being charged by many institutions while another 50% respondents said that it does partially justify the high fees.

3.  Given a choice to pay whatever amount they like after the education has been provided 20% of the respondents said that they would pay less than 5% of the indicated fee, another 40% respondents said that they would pay between 5% to 25% of the indicated fee and 12% respondents said that they would pay between 25% - 50% of the indicated fee. Among the 38% respondents who said they would pay at least half the indicated fee about 9% said that they would pay the indicated fee or more.

4. When asked about the amount they would pay if they are allowed to pay any amount but only before the education is provided, 99% of the respondents said they would pay the same or a lesser amount as they would do if they are allowed to pay after the education is provided. Of these an overwhelming 84% said that they would "lesser" or "much lesser" amount.

5. The last question asked was to see if the amount they would like to pay before the education is provided changes, if the selection is made dependent on the donation amount. In other words, those who donate more has higher chance of being selected for undergoing the programme. As expected about 47% of the respondents said that they would pay a larger amount in this situation than in the case when the donation amount has no linkage with the selection probability.      

I intend to do some more indicative surveys in future and will keep you posted of the findings.

Growth Stories

A snapshot of the past and present:

                                       Per Capita GDP (US$)        
                        1964    2013    CAGR
USA                 3574     53042   5.5%    
India                  118      1499   5.2%
Argentina          1166   14715    5.2%
Botswana            71.8   7315     9.6%
China                  84.6   6807     9.2%

Is a change of approach required?

Notes: 1. India and Argentina have very similar land areas
          2. Botswana is considered to be one of the safest countries in
             Africa
          3. PGPM of IIMA started in 1964

Thank you.

INR-USD exchange rate

I was doing some back-of-the-hand calculations on what could be a stable value of the US$-INR exchange rate.

I would not be surprised if it goes as low INR 74 to  1 US$. The reason for this is the falling value of Rupee in the last 9 years. Using the inflation figures of India and US, I find that the value of Rupee has depreciated by about 50% in this period where as that of US$ has depreciated by about 20%. In Aug 2004 the exchange rate was around INR 46 to 1 US$. This implies the current exchange rate should be around 46 x 0.8 x 2 = 73.6 i.e. around INR 74 to 1 US$. Since the current rates are hovering around INR 69 to 1 US $ I expect this to dip further in the coming weeks.

    

INR-USD exchange rate

The INR-USD exchange rate has been in news for the last few weeks. The question in every one mind seems to be how low can it go? What is the chance that it would cross  INR 60 per USD  in the next three months?

Based on the last 10 years data it seems that the chance of rupee breaching the INR 60 per USD mark is 13.5%. That's about 1 in 7. Quite possible in other words.

The chance of it crossing INR 62 per USD in the next three months is about 1%.

In his article "Optimum Strategies for Creativity and Longevity" Dr. Sing Lin gives an interesting actuarial table of Retirement Age and Age at Death which is reproduced below:

Retirement Age		Age at Death
49.9		86
51.2		85.3
52.5		84.6
53.8		83.9
55.1		83.2
56.4		82.5
57.2		81.4
58.3		80
59.2		78.5
60.1		76.8
61		74.5
62.1		71.8
63.1		69.3
64.1		67.9
65.2		66.8

A quadratic regression model can be nicely fitted to this data:

Age of Death = - 121.2 + 8.335 Retirement Age - 0.08394 Retirement Age**2

S = 0.713363 R-Sq = 99.0% R-Sq(adj) = 98.8%

It seems that one should plan to retire by 58 or 60 to benefit from the fruits of his /her hard work.

Odds for ICC World Cup Win

I found the following at this site : http://www.cricket-worldcup.net/finals.html

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India v Sri Lanka Win Betting - 02/04/11

• Sri Lanka v India - 02/03/11

India are 4/6 to win, Sri Lanka are 6/5 to win with Boylesports

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If converted to probability this means that probability of India winning is 0.4 and that for Sri Lanka winning is 0.545. It is interesting to observe that these two probabilities do not add up to 1.

Suppose now the betting house sells one bet of $100 for India winning to A and another bet of $100 on Sri Lanka winning to B.

Then in case India wins the betting house returns $100 (to A) and pays out $150 additional (to A). It keeps $100 of B. So the net loss for the house is $50.

In case SriLanka wins the betting house returns $100 (to B) and pays out $83.33 (to B). It keeps $100 of A. So the net gain for the house is $16.77

How is the betting house going to make money then? The answer possibly is that it expects lot more gamblers to bet on Sri Lanka winning than on India winning. This can be explained from prospect theory. Since, the chance of Sri Lanka winning is more than that of India winning, for a gambler the chance of losing $100 is more when betting for India than for Sri Lanka. This will drive a larger number of gamblers to bet for Sri Lanka. The fact that they (gamblers) stand to gain about 80% more if they win by betting for India than for Sri Lanka is likely to be overridden by the fact that the chance of losing of $100 is 32% more when betting for India than for Sri Lanka.

An interesting illustration of Prospect Theory is practice !!!

Will Sensex hit 21000 before Diwali?

I saw a news item in a newspaper website speculating that the Sensex will cross 21000 prior to Diwali. As per my calculations the chance is not that bright. It is only about 9%.

Here is the probability distribution of the value of Sensex on the pre-Diwali day:

Less than 19000 - 5%

Between 19000 to 19500 - 14%

Between 19500 - 20000 - 28%

Between 20000 - 20500 - 26%

Between 20500 - 21000 - 18%

Above 21000 - 9%

Happy Diwali!