Hypothesis Testing Ppt by Sharad
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Transcript of Hypothesis Testing Ppt by Sharad
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HYPOTHESIS TESTING
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HYPOTHESIS
It is a tentative prediction or explanation of two or more variables
The hypothesis is the most important mental tool the research has
It is important integral component of modern scientific research
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Set up a hypothesis
Set u
p a
suit
able
si
gnif
ican
ce le
vel
Setting a test criteria
Doing
Com
putations
Making Decisio
ns
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TYPES OF ERRORS:
Ho is True Correct Decision Type I Error
Ho is False Type II Error Correct Decision
Accept Ho Reject Ho
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ESTIMATION THEORY Estimating about population from a sample drawn
is estimation TWO TYPES: POINT ESTIMATE INTERVAL ESTIMATE METHODS OF ESTIMATING PARAMETERS:
Test the significance for attributes Test of significance for variables (large
samples) Test of significance for variables (small
samples)
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TEST OF SIGNIFICANCE FOR ATTRIBUTES
Test for number of success Test for proportion of success Test for difference between proportions
1. TEST FOR NUMBER OF SUCCESS:Standard Error(S.E.) for number of success =
npqWhere: n = size of sample p = probability of success in each trial q = probability of failure (1-p)
Hypothesis testing: Difference/ S.E.
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2.TEST FOR PROPORTION OF SUCCESS:
Here we record proportion of success instead of number of
success
S.E. = pq / n
Limits are given as
[ p 3 pq / n] X 100
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3.TEST FOR DIFFERENCE BETWEEN PROPORTIONS:
If two samples are drawn from different populations, we may
be interested in finding out whether the difference between the
proportion of success is significant or not.
S.E.(p1 – p2) = 1/pq ( 1/n1+ 1/n2 ),
Where, p = n1p1+n2p2/ n1+n2
Hypothesis testing :Difference (p1 – p2)/ S.E.
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TEST OF SIGNIFICANCE FOR LARGE SAMPLE
(when mean and standard deviation is given)
Standard Error of Mean
S.E.X = / n
Fiducial limits of population mean:
At 95% X 1.96 S.E.
At 99% X 2.58 S.E.
Standard Error of Mean of two samples:
S.E.X1- X2 = 12 / n1 + 2
2 /n2
Difference = Difference of mean
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TEST OF SIGNIFICANCE FOR small SAMPLE
Test the significance of the mean in a random sample
Formula: t = (X - / S) X n
S = √ d2
n-1
Where X = the mean of sample
= the actual or hypothetical mean of the population
n = sample size
S = std deviation of the sample.
d = deviation from mean.
Also degree of freedom = n-1
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Fiducial limits of the population:
At 95% Significance level
X ( S )t 0.05
n
At 99% Significance level
X ( S )t 0.01
n
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Testing the significance of difference between two sample means – small sample:
In this it is assumed that the two samples are independent that is the value of observation in one sample does not depend on other.
Formulae: t = X1 - X2 x n1n2
S n1 + n2
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X1 = mean of the first sample
X2 = mean of second sample
n1 = number of observation in first sample
n2 = number of observation in second sample
S = combined std deviation (dev should be from actual mean)
S = (X1 – X1)2 (X2 – X2)2
n1 + n2 - 2
D.f = n1 + n2 - 2
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CHI SQUARE TESTFormulaFormula
2 = ∑ (O – E)2
E
2 = The value of chi squareO = The observed valueE = The expected value
∑ (O – E)2 = all the values of (O – E) squared then added together
Degree of Freedom: (r-1)(c-1) or (n-1)