Probability and Statistics

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Probability and Statistics

Postby Biosapien on August 2nd, 2016, 5:40 am 

Hi everyone,

I am having a great trouble in understanding statistics for long time can some one help me to understand the basic concepts of statistics or bio statistics which builds a great foundation for my research profession. I am started to learn statistics with the chapter called Probability. I understand the basic concept of Probability but struggling a bit to understand the concept of dependent event and independent event, can some one explain me what is mean by dependent and independent events. Thank you
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Re: Probability and Statistics

Postby doogles on August 3rd, 2016, 6:08 pm 

I'm surprised that you did not get an answer to this Biosapien. I'm not a statistician, but I have a working understanding of statistics.

I couldn't help thinking about your question. It occurred to me that in point of fact nobody ever uses the words dependency and independency when reporting the statistical results of studies or research. Such a notion implies a sort of cause and effect, which is just 'not on' when reporting the results of statistical analyses. The best we can say scientifically is that there is significant (or non-significant) association between two measurable sets of data. This then becomes 'evidence' of an association, but certainly not of a cause and effect.

I think that the only time you will see these terms used is in exams on their meaning when doing elementary statistics. If that is the case, then the terms 'dependency' and 'independently' become just another lot of useless padding that seems to crop up in many subjects.

What I've just said won't help your understanding at all. But let me try to give an example of what I mean.

We all believe now that sunlight is essential for the growth of plants. And it's one of those fairly 'sure' things in life. Supposing you wished to check if the growth rate of plants was associated with the amount of natural direct sunlight at any given time. You can get figures on the amount of sunlight reaching any square kilometre of the planet each day or month from weather bureau data and you could plant something like sunflowers whose rate of growth you could actually measure and average each day.

Now in elementary statistics, the amount of natural direct sunlight (in megajoules per square kilometre) would be the INDEPENDENT variable because it is produced by factors independent of your control (It's natural direct sunlight you are measuring). You wish to find out how much the daily rate of growth of the sunflowers is dependent on the daily amount of direct sun (Obviously clouds and particulate matter may change this), so in this case the rate of daily growth of the sunflowers is the DEPENDENT variable.

But in fact, you will finish up with a data set of daily insolation (This is the term for sunlight reaching the Earth's surface) and a data set of daily growth rates of sunflowers (obviously you must keep the sunflowers in a stable condition of water and nutrients). Then you would graph the average daily growth rates of your plants against the average daily insolation in your part of the globe and use software to do a statistical correlation, along with it's significance. Nowhere in the results would DEPENDENCY or INDEPENDENCY be mentioned.

But esoterically, and with no real practical value, you could say that the growth rate of the sunflowers was dependent on the amount of sunlight reaching the plot daily, a factor that was acting independently of your control.

You could use two plots of sunflowers. Leave one with the basics and add some boron to the soil in the other. The you would have the opportunity to compare the growth rates with and without added boron. You would finish up with two data sets for the sunflowers. And you would compare the two sets of results statistically.

If there was a statistically significant difference between the two plots, all you would report is that there was a significant difference between the two groups. DEPENDENCY and INDEPENDENCY are not mentioned. Again, esoterically, once the boron has been added, it becomes the independent variable, because you can't change it, and the growth rate becomes dependent on the addition of boron.

I've left out a number of ifs and buts for simplicity, but in practice, it doesn't matter which is Dependent, and which is Independent. And in many cases, it's difficult to say which is which.

I hope this is of some help and not adding to the confusion.
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Re: Probability and Statistics

Postby Lomax on August 3rd, 2016, 9:35 pm 

Hi Biosapien,

I don't take issue with what doogles says but it leaves out a (related) definition of dependence which is commonly used in statistics. (Disclaimer: I'm not a statistician either, although I did the first year of a mathematics degree.) Independence can be a property not just of variables, but of the values of those variables.

We talk of a single datum being independent if it doesn't rely on a previous datum (for the same variable). Think of the gambler's fallacy: many gamblers believe that if they lost the last ten rolls of the dice they're surely due a win on the next one. Actually, the outcome of the next roll is not affected by the outcome of the last one. In this sense all rolls are independent, not of their external conditions but of each other. A counter-example would be if you had ten men and ten women, and you chose three at random - the odds of your third choice being male depend on whether you first two were male, female, or one of each.

Mathematically, the probability P of two independent events (A) and (B) occurring can be expressed as

P(A & B) = P(A)P(B)

(The probability of both A and B occurring is equal to the probability of A occurring multiplied by the probability of B occurring.) So if each has a 0.5 probability (for example), then the probability of both is (0.5)(0.5), or 0.25. Any values/data/events which do not follow this rule are said to be dependent.
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Re: Probability and Statistics

Postby Biosapien on August 3rd, 2016, 11:37 pm 

Hi Doggles and Lomax

Thanks for both of you for deeply explaining the facts about the query which i ve raised. Though doggles explained more about significant or P value rather than dependent and independent event, it's quite interesting to learn the basic which he explicit. What Lomax described is more relevant to my query. Like biology i am unable to raise the why in the subject of bio statistics and the worse thing is applying the formula for a given situation to predict the outcome. For any further queries i will text you guys sooner or later. I appreciate both of you for your kind reply. Thank you
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