Statistics- Important Points to remember

STATISTICS

Some important points:

Ø F distribution is coined by George W Snedewr in Honour of Sir Ronald a fisher.

Ø Chi square (non parametric test) concept given by karl pearson.

Ø Concept of normal distribution is given by De Mouire and person involved in this are laplace, gauss and W J Yoden.

Ø Concept of regression is given by Sir francis galton in 1877.

Ø Concept of T- distribution is given by WS Gooset.

Ø Data which are collected for the first time are primary data.

Ø Data is only quantitative.

Ø Secondary data are second hand data which are in the form of published & unpublished.

Ø Category of secondary data are also called paper source.

Ø Median and mode are positional average.

Ø Arthemetic mean , geometric, harmonic & weighted average mean are mathematical average.

Ø ∑ know as capital sigma.

Ø Property of arthemetic mean-:

1)   Sum of all observations of the given set of observations from their arthemetic mean is zero.

2)   Combined mean= n1x1 + n2x2/n1+n2

3)   The sum of square of the deviations of the given set of observations is minimum when taken from the arthemetic mean.

4)   Mean is affected by both change of scale and change of origin.

5)   AM> GM> HM ( AM- arthemetic mean, GM- geometric mean, HM- harmonic mean)

6)   Mode = 3median – 2mean

7)   One dimensional 1d diagram are those which have only length. Examples are line diagram, multiple bar diagram, compound or cluster bar diagram, sub divided bar diagram are also called component bar diagram, percentage bar diagram, deviationa bar diagram.

Ø Two dimensional diagram are those in which both length and breadth are present 2D. Examples are histogram, area diagrams, rectangles, square, circles and pie diagram.

Ø Ogive curve and frequency polygon are also 2d diagrams.

Ø Ogive represent cumulative frequency and histogram frequency distribution and frequency polygon means many angled diagrams.

Ø 3D , three dimensional diagrams are those cubes, sphere, cylinders and cuboid.

Ø Numerical characteristics of population are parameters and sample are sample statistics/ estimators.

Ø Random sampling method is also called probability sampling method.

Ø Non random sampling method is also called non probability sampling method.

Ø Random sampling methods are

1)   Simple random sampling method

2)   Stratified random sampling method

3)   Systematic sampling method

4)   Cluster sampling method

5)   Multistage sampling

Ø Non random sampling methods are

1)   Convenience sampling or chunk or incidental sampling

2)   Judgement sampling

3)   Purposive sampling

4)   Quota sampling

5)   Snow ball sampling

Ø The larger the sample the more accurate will be the research.

Ø Increasing the sample size decreases the sample error.

Ø Sample size N = 100

Ø Principles of sampling-

1)   Law of statistical regularity

2)   Principle of inertia of large number

3)   Principles of persistence of small numbers

4)   Principle of validity

5)   Principle of optimization

Ø Type 1 error by rejecting a true null hypothesis and it is also known as producer error, alpha or level of significance.

Ø Type 2 error by accepting the false null hypothesis also called consumer error ( 1- β) beta, power function of test or power curve, power of test.

Ø Standard error ( SE) is standard deviation of the distribution of the sample mean. S.E = σ/√n

Ø In a normal distribution curve, since the curve is a bell shaped & symmetrical i.e mean=median=mode

Ø Total area under normal probability curve is 1 ( .5 + .5)

Ø Since curve is symmetrical co efficient of kurtosis is 3 mesocurtic.

Ø Range of distribution is ∞to ∞ but practically it is 6σ.

Ø Point of inflexion is x= +- µσ

Ø Leptokurtic <3, platokurtic>, mesocurtic =3.

Ø Area µ+-1σ= 68.27%, µ+- 2 σ= 95.45%, µ+- 3σ= 99.73%

Ø Z( standard normal distribution) = x-µ/σ

Ø Concept of binomial distribution is given by James bernoulli

Ø Concept of poisson distribution is given by simeon poisson . In this the value of mean and variance is (0,0)

Ø Standard deviation is also known as root mean square deviation.

Ø Standard deviation is affected by change of scale & independent of change of origin.

Ø Positively skewed= mean>median>mode.

Ø Negatively skewed= mode>median>mean.

Ø Balance pattern= mean=median=mode.

Ø Skewness means lack of symmetry or asymmetrical distribution.

Ø Concept of co efficient of skewness given by karl pearson

Ø Confidence interval 95%= 1.96, 99%= 2.56/2.58

Ø Z test is also called standard normal variable test, standard normal deviate test, approximation test, large scale test.

Ø Conditions to be applied in z test is-

1)   N> 30

2)   N≤30 ( standard deviation of population mean is given)

Ø One tailed test is also known as direction test or right tailed test. F test and chi square test is one tailed test.

Ø Two tailed test is called left tailed test as direction is not mention.

Ø Conditions to apply t test-

1)   N≤30 standard deviation of sample mean is given.

2)   To check the difference in mean.

Ø T test is also called t distribution & student t test, exact test, small test.

Ø Conditions to accept & reject hypothesis-:

1)   Table value> calculated value= accept

2)   Table value< calculated value= reject

Ø Chi square is a non- parametric test

Ø Chi square lies from 0 to ∞

Ø Conditions to apply chi square test:-

1)   Population mean & sample mean is not given in the question.

2)   Degree of freedom ( df-1) as df starts from t test.

Ø Chi square test is also known as :-

1)   Goodness of fit accumulation

2)   Contingency table

3)   Quantitative variables

4)   Co efficient of association

Ø Degree of freedom = ( row-1) ( column -1)

Ø F test in which value of numerator is always greater than denominator.

Ø Conditions to apply f test:-

1)   Population mean, sample mean & standard deviation is not given in the question.

2)   It will talk about two mean.

3)   Its value lies between 0 to ∞

Ø Concept of correlation is given by karl pearson.

Ø Correlation denotes from R and its values lies between -1 to 1

Ø Spearman correlation given by Edward spearman.

Ø Edward spearman denotes correlation from p ( rho)

Ø P= 1- 6∑d2/n (n2-1)

Ø If tied rank the formula will be p= 1-6∑d2/n(n2-1) + m(m2-1)/12

Ø Karl pearson correlation formula is cov( xy)/σx.σy

Ø Correlation is independent of both change of scale & origin.

Ø Regression is affected by change of scale & independent of change of origin.

Ø R2 is coefficient of determination.

Ø Coefficient values lies between 0 to 1.

Ø R2= bxy* byx

Ø Regression shows a causual effect i.e cause & effect relationships.

Ø Parametric test:-  z test, t test, f test.

Ø Non parametric test or distribution free test:- sign test, median test, mann whitney u test, run test, k.s test, chi square test.

Ø Paired t test is used in management training, special coachings, producti

Ø vity of crop before & after.

Ø Paired t test is also known as bivariate normal distribution.

Ø Nominal scale=mode used, ordinal scale= mode & median, interval & ratio scale = mean, median, mode. 

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