Ppt

1. There are two types of statistical inferences:
Estimation of population parameters and hypothesis
testing.
Hypothesis testing is one of the most important tools of
application of statistics to real life problems.
Most often, decisions are required to be made
concerning populations on the basis of sample
information.
Statistical Inference

2. Tests of differences between groups (independent
samples);
Tests of differences between variables (Pre to
Post) (dependent samples);
Tests of relationships between
variables.(Quantitative)
Association between factors

3. Parametric Tests
Data approximately normally distributed.
Dependent variables at interval level.
Sampling: random
t - tests
ANOVA(F test),
Z test

4. Non-parametric Tests
Do not require normality
Ordinal ,Nominal Or interval level of measurement
Less Powerful -- probability of rejecting the null
hypothesis correctly is lower.
So use Parametric Tests if the data meets those
requirements.

5. Non parametric tests:
Mann-Whitney U test
Wilcoxon Signed rank sum test
Kruskal-wallis test
Chisquare test

6. Chi-Square as a Statistical Test
Chi-square test: an inferential statistics
technique designed to test for significant
relationships between two variables organized in
a bivariate table.
Chi-square requires no assumptions about the
shape of the population distribution from which a
sample is drawn.

7. Chisquare test…….
A statistical method used to determine
goodness of fit
Goodness of fit refers to how close the
observed data are to those predicted from a
hypothesis

8. Hypothesis Testing with Chi-Square
Chi-square follows five steps:
1. Making assumptions (random sampling)
1. Stating the research and null hypotheses
1. Selecting the sampling distribution and specifying the
test statistic
1. Computing the test statistic
1. Making a decision and interpreting the results

9. Stating Research and Null Hypotheses
The research hypothesis (H1) proposes that the
two variables are related in the population.
The null hypothesis (H0) states that no association
exists between the two cross-tabulated variables in
the population, and therefore the variables are
statistically independent.

10. The Chi Square Test
The general formula is
χ2 = Σ
(O – E)2
E
• where
– O = observed data in each category
– E = Expected data in each category
– Σ = Sum of the calculations for each category

11. Calculating Expected Frequencies
To obtain the expected frequencies for any cell in any
cross-tabulation in which the two variables are
assumed independent, multiply the row and column
totals for that cell and divide the product by the total
number of cases in the table.
E = (column Total) x (row Total)
N

12. Determining the Degrees of Freedom
df = (r – 1)(c – 1)
where
r = the number of rows
c = the number of columns

13. The Sampling Distribution of Chi-Square
Chi-square values are always positive. The
minimum possible value is zero, with no upper limit
to its maximum value.
As the number of degrees of freedom increases, the
χ2 distribution becomes more symmetrical.

14. Interpretation:
If our calculated value of chi square is less than the
table value, accept or retain Ho
If our calculated chi square is greater than the
table value, reject Ho
…as with t-tests and ANOVA – all work on the
same principle for acceptance and rejection of the
null hypothesis

15. Ex 1:For the following data determine if there is any
association between trachoma and Corneal
degeneration
(X2 = 3.841 under probability of 0.05)
Trachoma No Trachoma Total
Corneal
degeneration
65 50 115
No Corneal
degeneration
25 60 85
Total 90 110 200

16. Ex:2
Test whether the prevalence of carriers of
Filariasis is associated with gender
Gender No. of carriers No. of non
carriers
Total
Males 85 415 500
Females 65 535 600
X2 value=3.841 with 1 d.f. And 95% confidence level

17. Limitations of the Chi-Square Test
The chi-square test does not give us much information
about the strength of the relationship or its substantive
significance in the population.
The chi-square test is sensitive to sample size. The size of
the calculated chi-square is directly proportional to the
size of the sample, independent of the strength of the
relationship between the variables.
The chi-square test is also sensitive to small expected
frequencies in one or more of the cells in the table.

18. Chi-Square Table