Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.
You know intuitively that there is a 50 per cent chance of getting heads, and 50 per cent chance of getting tails. Divide this by the total number of possible outcomes. Yet you could toss a coin 10 times and get seven heads and three tails, which is 70 per cent heads and 30 per cent tails.
However, if you toss that coin 1, times or more — which a few people have done — you will eventually begin to see that breakdown. This illustrates another important point about probability. It depends on the outcome or event happening over a large number of repetitions, or with a large number of people. There are many examples of how probability is used throughout society. One common measure is the probability of developing cancer.
Producing data —how data are obtained and what considerations affect the data production process. Exploratory data analysis —tools that help us get a first feel for the data by exposing their features using graphs and numbers. To really understand how inference works, though, we first need to talk about probability , because it is the underlying foundation for the methods of statistical inference.
We use an example to try to explain why probability is so essential to inference. First, here is the general idea: As we all know, the way statistics works is that we use a sample to learn about the population from which it was drawn. Ideally, the sample should be random so that it represents the population well. Recall from Types of Statistical Studies and Producing Data that when we say a random sample represents the population well , we mean that there is no inherent bias in this sampling technique.
Unfortunately, when looking at a particular sample which is what happens in practice , we never know how much it differs from the population. This uncertainty is where probability comes into the picture. We use probability to quantify how much we expect random samples to vary. Before knowing statistical decision procedures one must have to know about the theory of probability. The characteristics of the Normal Probability. Curve is based upon the theory of probability. Normal Distribution is by far the most used distribution for drawing inferences from statistical data because of the following reasons:.
Number of evidences are accumulated to show that normal distribution provides a good fit or describe the frequencies of occurrence of many variables and facts in i biological statistics e. Normal distribution is of great value in evaluation and research in both psychology and education, when we make use of mental measurement.
It may be noted that normal distribution is not an actual distribution of scores on any test of ability or academic achievement, but is instead, a mathematical model. The distribution of test scores approach the theoretical normal distribution as a limit, but the fit is rarely ideal and perfect.
When we toss an unbiased coin it may fall head or tail. If we toss two unbiased coins, they may fall in a number of ways as HH two heads HT 1st coin head and 2nd coin tail , TH 1st coin-tail and 2nd coin head or TT two tails.
So there are four possible arrangements if we toss two coins, a and b , at the same time:. In a similar manner if we toss ten coins, and substitute 10 for n , the binomial expansion will be. The expansion has eleven combinations and the chance of occurrence of each combination out of the total possible occurrence is expressed by the coefficient of each combination.
We can represent the above eleven terms of the expansion along X-axis at equal distances as:. We can represent the chance of occurrence of each combination of H and T as frequencies along Y axis.
If we plot all these points and join them we shall get a symmetrical frequency polygon. Carefully look at the following frequency distribution, which a teacher obtained after examining students of class IX on a mathematics achievement test see Table 6. Are you able to find some special trend in the frequencies shown in the column 3 of the above table?
Probably yes! If we draw a frequency polygon with the help of the above distribution, we will have a curve as shown in Fig. This normal curve has great significance in psychological and educational measurement. In measurement of behavioural aspects, the normal probability curve has been often used as reference curve. Thus, the normal probability curve is a symmetrical bell-shaped curve. In certain distributions, the measurements or scores tend to be distributed symmetrically about their means.
That is, majority of cases lie at the middle of the distribution and a very few cases lie at the extreme ends lower end and upper and. In other words, most of the measures scores concentrate at the middle portion of the distribution and other measures scores begin to decline both to the right and left in equal proportions. This is often the case with many natural phenomena and with many mental and social traits. If we draw a best fitting curve for such symmetrical distribution it will take the shape of a bell-shaped curve symmetrical on both sides of its centre.
Statistics , Normal Distribution , Probability. Divergence that Occur in the Normal Curve Statistics. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits.
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