What is statistical inference, Advanced Statistics

What is statistical inference?

 Statistical inference can be defined as the  method of drawing conclusions from data which are subject to random variations. This is based on the mathematical laws of probability. Probability is the branch of statistics, where we make inferences from a finite set of observations to an infinite set of new observations. The finite set of observations is called as Samples and the infinite set is called as populations. Suppose let us consider tossing a few coins. Here the total number of outcomes i.e., getting the heads and tails are called as the sample space. The new observation that is getting particularly heads or tails is the population.

Solutions to statistical inference:

There are two kinds of statistical inferences. One is the estimation, where we use the sample and sample variables to predict the population variables. The second is the hypothesis testing. Here we use the samples and sample variables to test the population and the population variables.


 Estimation can be divided into two types. One is point estimation and the other is interval estimation.  In the point estimation we use the sample variable to estimate the parameter ?, whereas in the interval estimation we use the samples variable to construct an interval which is equated to p where p is the confidence level adopted.

The most common method adopted for point estimation is the maximum likelihood estimation (MLE) which consists of choosing the estimate that maximizes the probability of the statistical material. MLE is the best solution if the statistical material is large. Special cases of MLE are the sample mean dented as E(X) and the relative frequency denoted by P(X=x).

Illustrations  of MLE:

A game is played with a single fair die. A player wins Rs.20 if a 2 turns up and Rs.40 if a 4 turns up, and he losses if a 6 turns up. While he neither wins nor loses if any other face turns up. Find the expected sum of money he can win.

Let X be the random variable denoting the amount he can win. The possible values are 20,40,-30,0

P[X=20] = P(getting 2) = 1/6

P[x=40] = P( getting 4 = )1/6

P[X = -30] = P(getting 6] = 1/6

The remaining probability is ½.

Hence the mean is E(X) = 20(1/6) + 40(1/6) + (-30)(1/6) +0(1/2) = 5.

Hence the expected sum of money he can win is Rs.5

Hypothetical Testing:

A statistical hypothesis is a statement of the numerical value of the population parameter.

The steps involved in solving a statistical hypothesis is

1.       State the null hypothesis Ho

2.       State the alternative hypothesis Ha

3.       Specify the level  of significance α

4.       Determine the critical regions and the appropriate test statistic.

5.       Compute the equivalent test statistic of the observed value of the parameter.

6.       Take the decision either to reject Ho or accept Ho.

Posted Date: 7/21/2012 9:16:51 AM | Location : United States

Related Discussions:- What is statistical inference, Assignment Help, Ask Question on What is statistical inference, Get Answer, Expert's Help, What is statistical inference Discussions

Write discussion on What is statistical inference
Your posts are moderated
Related Questions
Baddeley'smetric : A manner of measuring the 'error' in the image processing technique or method. The metric is derived using the fundamental theory from the stochastic geometry an

Q. A toothpaste company want to know if its new product increases the length of time in-between dentist visit to its user. The company sets a target for 180 days to determine if it

Literature controls : The patients with the disease of interest who have received, in the past, one of two treatments under the investigation, and for whom the results have been pu

Kolmogorov Smirnov two-sample method is a distribution free technique which tests for any difference between the two populations probability distributions. The test is relied on t

Incubation period is the time elapsing amongs the receipt of infection and the appearance of the symptoms. The length of the incubation time period depends on the disease, ranging

Demographic data: Age: continuous variable Gender: categorical variable with males coded 1, females coded 2. Relationship status: categorical variable 1 to 5. Rational

Multi dimensional unfolding is the form of multidimensional scaling applicable to both the rectangular proximity matrices where the rows and columns refer to the different sets of

Ha: If hyperlipidemia is believed to be a side effect of second-generation antipsychotics (SGAs), then Hispanic patients with SGAs treatment will have the higher frequency of devel

Multidimensional scaling (MDS)  is a generic term for a class of techniques or methods which attempt to construct a low-dimensional geometrical representation of the proximity matr