PSYCHOLOGICAL STATISTICS FINALS (CHI SQUARE)

Parametric Test

The test in which, the population constants like mean, std deviation, std error, correlation coefficient, proportion etc. and data tend to follow one assumed or established distribution such as normal, binomial, poisson etc,

Non parametric Test

the test in which no constant of a population is used. Data do not follow any specific distribution and no assumption are made in these tests

e.g . to classify good, better, best we just allocate arbitrary numbers or marks to each category

Hypothesis

A definite statement about the population parameters

Null hypothesis (H ₀₎

States that no association exists between the two cross-tabulated variables in the population, and therefore the variables are statistically independent.

Alternative Hypothesis (H_a or H₁₎

Proposes that the two variables are related in the population.

Degree of freedom

It denotes the extent of independence (freedom) enjoyed by a given set of observed frequencies

Contingency Table

When the table is prepared by enumeration of qualitative data by entering the actual frequencies and it that table represents occurance of two sets of events, that table is called the ____ ____.

Chi-square Test

• an important test among the several tests of significance developed by statisticians

• a non parametric test not based on any assumption or distribution of any table

• the test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis

Karl Pearson

He developed the Chi-Square Test in 1900

Applications of a Chi-Square Test

1. Goodness of fit of distributions

2. test of independence of attributes

3. test of homogenity

TEST OF GOODNESS OF FIT OF DISTRIBUTIONS

This test enables us to see how well does the assumed theoretical distribution (such as Binomial distribution, Poisson distribution or Normal distribution) fit to the observed data.

TEST OF INDEPENDENCE OF ATTRIBUTES

Test enables us to explain whether or not two attributes are associated

TEST OF HOMOGENITY

This test can also be used to test whether the occurance of events follow uniformity or not