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Why Normal distribution is better then other distributions in statistics?
Wiki User
∙ 14y ago
The normal distribution has two parameters, the mean and the standard deviation Once we know these parameters, we know everything we need to know about a particular normal distribution. This is a very nice feature for a distribution to have. Also, the mean, median and mode are all the same in the normal distribution. Also, the normal distribution is important in the central limit theorem. These and many other facts make the normal distribution a nice distribution to have in statistics.
Wiki User
∙ 14y ago
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Why normal distribution is better than other distributions?
It may not be better, but there is a lot of information on the normal distribution. It is one of the most widely used in statistics.
Why you prefer normal distribution as compare to others in statistics?
Perhaps a mistaken impression, after completing an initial course in statistics, is that one distribution is better than another. Many other distributions exists. Usually, introductory statistics classes concern confidence limits, hypothesis testing and sample size determination which all involve a sampling distribution of a particular statistic such as the mean. The normal distribution is often the appropriate distribution in these areas. The normal distribution is appropriate when the random variable in question is the result of many small independent random variables that have been are summed . The attached link shows this very well. Theoretically, a random variable approaches the normal distribution as the sample size tends towards infinity. (Central limit theory) As a practical matter, it is very important that the contributing variables be small and independent.
When it comes to comparing data from different distributions what is the benefit of normal standard distribution?
There may or may not be a benefit: it depends on the underlying distributions. Using the standard normal distribution, whatever the circumstances is naive and irresponsible. Also, it depends on what parameter you are testing for. For comparing whether or not two distributions are the same, tests such as the Kolmogorov-Smirnov test or the Chi-Square goodness of fit test are often better. For testing the equality of variance, an F-test may be better.
How do you check for normal distribution?
There are two main methods: theoretical and empirical. Theoretical: Is the random variable the sum (or mean) of a large number of imdependent, identically distributed variables? If so, by the Central Limit Theorem the variable in question is approximately normally distributed. Empirical: there are various goodness-of-fit tests. Two of the better known are the chi-square and the Kolmogorov-Smirnov tests. There are others. These compare the observed values with what might be expected if the distribution were Normal. The greater the discrepancy, the less likely it is that the distribution is Normal, the smaller the discrepancy the more likely that the distribution is Normal.
Explain how you could create a distribution of means by taking a large number of samples of four individuals each?
As the sample size increases, and the number of samples taken increases, the distribution of the means will tend to a normal distribution. This is the Central Limit Theorem (CLT). Try out the applet and you will have a better understanding of the CLT.
Why normal distribution is better than other distributions?
It may not be better, but there is a lot of information on the normal distribution. It is one of the most widely used in statistics.
Why you prefer normal distribution as compare to others in statistics?
Perhaps a mistaken impression, after completing an initial course in statistics, is that one distribution is better than another. Many other distributions exists. Usually, introductory statistics classes concern confidence limits, hypothesis testing and sample size determination which all involve a sampling distribution of a particular statistic such as the mean. The normal distribution is often the appropriate distribution in these areas. The normal distribution is appropriate when the random variable in question is the result of many small independent random variables that have been are summed . The attached link shows this very well. Theoretically, a random variable approaches the normal distribution as the sample size tends towards infinity. (Central limit theory) As a practical matter, it is very important that the contributing variables be small and independent.
When it comes to comparing data from different distributions what is the benefit of normal standard distribution?
There may or may not be a benefit: it depends on the underlying distributions. Using the standard normal distribution, whatever the circumstances is naive and irresponsible. Also, it depends on what parameter you are testing for. For comparing whether or not two distributions are the same, tests such as the Kolmogorov-Smirnov test or the Chi-Square goodness of fit test are often better. For testing the equality of variance, an F-test may be better.
How normal distribution is better?
Normal distribution is not "better." It is, perhaps, simpler to work with. All introductory text books and courses on statistics cover it in great detail, its properties are well-known, and there are lots of tables you can refer to. But if the real-world situation you are trying to model does not resemble a normal distribution, then it is very bad to try to use the properties of a normal distribution or to try to force a normal distribution on your data. Doing so will give you inaccurate answers.
What are advantages of inferential statistics?
They give estimates of unknown parameters which can then be used to make predictions based on distributions which are better known.
How do you check for normal distribution?
There are two main methods: theoretical and empirical. Theoretical: Is the random variable the sum (or mean) of a large number of imdependent, identically distributed variables? If so, by the Central Limit Theorem the variable in question is approximately normally distributed. Empirical: there are various goodness-of-fit tests. Two of the better known are the chi-square and the Kolmogorov-Smirnov tests. There are others. These compare the observed values with what might be expected if the distribution were Normal. The greater the discrepancy, the less likely it is that the distribution is Normal, the smaller the discrepancy the more likely that the distribution is Normal.
What are the advantages and disadvantages of nonparametric statistics compared to the parametric statistics?
Non-Parametric statistics are statistics where it is not assumed that the population fits any parametrized distributions. Non-Parametric statistics are typically applied to populations that take on a ranked order (such as movie reviews receiving one to four stars). The branch of http://www.answers.com/topic/statistics known as non-parametric statistics is concerned with non-parametric http://www.answers.com/topic/statistical-model and non-parametric http://www.answers.com/topic/statistical-hypothesis-testing. Non-parametric models differ from http://www.answers.com/topic/parametric-statistics-1 models in that the model structure is not specified a priori but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters but that the number and nature of the parameters are flexible and not fixed in advance. Nonparametric models are therefore also called distribution free or parameter-free. * A http://www.answers.com/topic/histogram is a simple nonparametric estimate of a probability distribution * http://www.answers.com/topic/kernel-density-estimation provides better estimates of the density than histograms. * http://www.answers.com/topic/nonparametric-regression and http://www.answers.com/topic/semiparametric-regression methods have been developed based on http://www.answers.com/topic/kernel-statistics, http://www.answers.com/topic/spline-mathematics, and http://www.answers.com/topic/wavelet. Non-parametric (or distribution-free) inferential statistical methodsare mathematical procedures for statistical hypothesis testing which, unlike http://www.answers.com/topic/parametric-statistics-1, make no assumptions about the http://www.answers.com/topic/frequency-distribution of the variables being assessed. The most frequently used tests include
Explain how you could create a distribution of means by taking a large number of samples of four individuals each?
As the sample size increases, and the number of samples taken increases, the distribution of the means will tend to a normal distribution. This is the Central Limit Theorem (CLT). Try out the applet and you will have a better understanding of the CLT.
What are the applications of statistics in education?
There are many applications of statistics in education. Statistics are used to better prepare students for the real world and testing for example.
What are application of statistics in education?
There are many applications of statistics in education. Statistics are used to better prepare students for the real world and testing for example.
What are the uses of median?
When someone asks a for an "average" value, that can mean a couple of different things. "Mean," "median," and "mode" are all values that are used to relate what the "center" or "average" of a distribution of values is. Each one has their advantages and disadvantages. The median is the value that divides the distribution exactly into halves - 50% is below it, and 50% above it. The median may not actually occur in the distribution, but it is the "balance point" of the distribution. The main advantage of the median is that it is not affected by outliers as the mean is and the mode can be. In distributions with a clear skew, such as housing prices or wages, using the median provides a much better estimate of what the "average" is.
What is better a signature or a normal Webkinz?
Normal Webkinz is better
