Null hypothesis AND ALTERNAT HYPOTHESIS

NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS

by- HARLEEN CHAWLA ( 47 ) HARMANDEEP KAUR( 48 )

NULL HYPOTHESIS

NULL HYPOTHESIS simply means “ NO DIFFERENCE”

The hypothesis says that OBSERVED DIFFERENCE IS ENTIRELY DUE TO SAMPLING ERROR i.e. it occurred purely by chance.

It is denoted by Ho.

AIM

In the test of significance ,null hypothesis is postulated to establish the basis for calculating the probability that the difference occurred purely of chance.

GENERAL PROCEDURE FOR TESTING A HYPOTHESIS

i. A NULL HYPOTHESIS ,suitable to problem is set up

ii. An alternate hypothesis is defined, if necessary.

iii. A suitable statistical test, using a relevant formula is calculated.

iv. The DEGREE OF FREEDOM is determined.

v. Then the probability value (p value) is found out, corresponding to the calculated value of test and its degree of freedom

vi. If ‘p value’ is less than 0.05 - test is NOT SIGNIFICANT.

vii. If ‘p value’ is more than 0.05- test is SIGNIFICANT

EVALUATION

TEST OF SIGNIFICANCE:

When the difference is significant-Null hypothesis is REJECTED

When the difference is not significant-Null hypothesis is NOT REJECTED i.e. approved.

The null hypothesis is never proved to be completely right or wrong, or true or false.

But it is only REJECTED or NOT REJECTED at the probability level of significance concerned.

GOALS Technical null hypotheses are used to verify statistical

assumptions. Scientific null assumptions are used to directly advance

a theory. i.e. to approve it.

Null hypotheses of homogeneity are used to verify that multiple experiments are producing consistent result

. It asserts the equality of effect of two or more

alternative treatments, for example, a drug and a placebo, are used to reduce scientific claims based on statistical noise. This is the most popular null hypothesis; It is so popular that many statements about significant testing assume such null hypotheses.

ALTERNATIVE HYPOTHESISIt is defined as the prediction that there

is a measurable interaction between variables

It is also called as “MANTAINED hypothesis” or “RESEARCH hypothesis”

It is denoted by H(a)Null hypothesis is opposed by alternative

hypothesis.When null hypothesis is rejected,

ALTERNATIVE HYPOTHESIS is not rejected and vice versa.

NORMAL DISTRIBUTION CURVE

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

Area under the curve can be represented in terms of relationship between and the standard deviation . The relationship is expressed as follows:

a) Mean +or- 1SD includes 68.3% of all observations.

b) Mean + or -2SD includes 94.4% of all observations.

c) Mean + or – 3 SD includes 99.7% of all observations.

CHARACTERISTICS

i. NDC has a peak in the centre with two tails on either side.

ii. The mean, median and mode of the distribution coincide and correspond to the peak of the distribution

iii. The curve is bell shaped and bilaterally symmetrical around the mean of the distribution

iv. The proportion of frequencies lying on either side of mean follows a specific type of pattern.

v. The area under normal curve is unity

or one.

vi. Standard deviation is one.

SKEWED DISTRIBUTION

When the frequency distribution or a frequency curve is not symmetrical about the peak , it is said to be SKEWED DISTRIBUTION.

In this one tail of the curve will be longer then the other.

This skewness can be either to the left or to thev right of the peak.

PROBABILITY

THE average relative frequency with which an event is expected to occur in the given population or universe.

It is denoted by “P”

SCALE OF PROBABILITY MEASUREMENTIt ranges from 0 to 1.

Zero is the minimum value –It represent absolute impossibility of occurrence of an event.

One is the maximum value - It represents absolute certainty of occurrence all the times.

FORMULA

IT CAN BE CALCULATED AS P=n(p)/N

WHERE , n(p) =no. of times the event occurred.

N= total no. of trials

Eg : probability of getting kings in a set of playing cards – 4/52 = 1/13

To find out probabilities in complex situation where the same event is happening in more than one ways and events concerned or independent, 2 rules are present-

i) ADDITION RULE

ii) MULTIPLICATION RULE

ADDITION RULE

If an event is occuring in mutually exclusive way in trial then the total probability of occurrence of that event in any way of trial is the sum of probabilities of the occurrence of that event in individual trial .

Mutual exclusive events –events that cannot occur simultaneously or present at same time. They follow this rule.

FORMULA : P ( A or B)=P (A) + P(B)

where A

and B are mutualy exclusive

Eg : what is the Probability of getting red or green colour balls from a set of 20 balls?

5 balls of each colour – red ,green ,blue and yellow respectively

Probability of getting red balls - 5/20 = 1/4

Probability of getting green balls - 5/20 = 1/4

Then total probability = sum of individual probabilities= ¼ + 1/4 = 2/4 = 1/2

MULTIPLICATION RULE

Independent events follow the multiplication rule of probability.

INDEPENDENT EVENTS : Two events are said to be independent ,if the absence or presence of one does not alter the chances of other being present, or if the occurrence of one does not alter the chance of occurrence of other.

FORMULA

MULTIPLICATION RULE: P(A & B)=P(A)*P(B)

if A and B are independent events.

Eg : what will be the probability of child being male and Rh negative?

Probability of a child born being male =P(1) = 1/2

Probability of child born being Rh negative = P(2) = 1/10 {10% children at birth may be Rh negative}

Probability of child being male and Rh negative

= P(1) * P(2) = 1/2 * 1/10 = 1/20 = 0.05

THANK YOU