HYPOTHESIS TESTING

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

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

TYPES OF ERRORS:

Ho is True Correct Decision Type I Error

Ho is False Type II Error Correct Decision

Accept Ho Reject Ho

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)

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.

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

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.

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

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

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

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

 

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

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)