**STAT-231: STATISTICAL METHODS**

**Credits: 2(1+1)**

**THEORY:**

Definitions of Statistics and its applications in Agriculture, limitations, types of **d**ata, classifications and frequency distribution, Histogram, frequency curve, frequency polygon, cumulative frequency curve (ogive curve)

Arithmetic mean, median, mode, GM, HM, weighted average, quartile, deciles, percentiles, Characteristics of ideal measure, merits and demerits of various measures (grouped and ungrouped data), Range, mean deviation, quartile deviation, standard deviation and variance and respective relative measures (grouped and ungrouped Data), Concept of measures of Skewness and Kurtosis.

Definitions of population, sample, parameter, statistic, need of sampling, sampling versus complete enumeration and introduction to simple random, stratified and multistage sampling methods. Simple random sampling with and without replacement.Use of random number tables for selection of simple random sample.

Random experiment, events (simple, compound, equally likely, complementary, independent) Definitions of probability (mathematical, statistical, axiomatic), addition and multiplication theorem (without proof). Simple problems based on probability, Random variable, discrete and continuous random variable, probability mass and density function, definition and properties of Binomial, Poisson and Normal distributions.

Null and alternate hypothesis, types of errors, degrees of freedom, level of significance, critical region, steps in testing of hypothesis, one sample, two sample and paired ‘t’ test. F test for equality of variance, Large sample tests for one sample mean, two sample means ‘Z’ tests, Chi-square test of goodness of fit, Chi-square test of independence of attributes in 2 X2 contingency table

Definition of correlation, types, scatter diagram. Karl Pearson’s coefficient of correlation and its test of significance. Spearman’s rank correlation coefficient, Linear regression equations, definition & properties of regression coefficient, constant, fitting of regression lines, its test of significance, comparison of regression and correlation coefficients

Introduction to analysis of variance, Assumptions of ANOVA, analysis of one way classification and two way classification

**PRACTICALS:**

Graphical presentation: Histogram, frequency curve, frequency polygon, cumulative frequency curve (ogive curve)

Computations of arithmetic mean, mode, median, GM and HM, quartiles, deciles&percentiles(Ungrouped data), Computations of arithmetic mean, mode, median, quartiles, deciles& percentiles (grouped data).

Computations of range, mean deviation, quartile deviation, standard deviation and variance and respective relative measures (ungrouped Data), Computations of range, mean deviation, quartile deviation, standard deviation and variance and respective relative measures (grouped data).

Selection of random sample using simple random sampling.

Computations of Karl Pearson’s coefficient of correlation with its test of significance, Spearman’s rank correlation, Fitting of simple linear regression equation with test of significance of regression coefficient.

Problems on One sample, two Sample and paired t-test, Chi-Square test of Goodness of Fit. Chi-square test of independence of Attributes for 2 X 2 contingency table.

Analysis of Variance one way and two way classification.

**Practicals (Experiments):**

1) **Graphical presentation: **Histogram, frequency curve, frequency polygon, cumulative frequency curve (ogive curve)

2) **Measures of central tendency**: Computations of arithmetic mean, mode, median, GM and HM, quartiles, deciles & percentiles (Ungrouped data)

3) Computations of arithmetic mean, mode, median, quartiles, deciles & percentiles (grouped data)

4) **Measures of Dispersion: **Computations of range, mean deviation, quartile deviation, standard deviation and variance and respective relative measures (ungrouped Data)

5) Computations of range, mean deviation, quartile deviation, standard deviation and variance and respective relative measures (grouped data)

6) Selection of random sample using simple random sampling

7) **Correlation: **Computations of Karl Pearsons coefficient of correlation with its test of significance

8) Spearman’s rank correlation

9 & 10) **Regression**: Fitting of simple linear regression equation with test of significance of regression coefficient

11) **Test of Significance: **Problems on One sample, two Sample and paired t-test

12) F test for equality of variance

13 & 14) Chi-Square test of Goodness of Fit. Chi-square test of independence of Attributes for 22 contingency table

15 & 16) **Analysis of Variance: **Analysis of Variance one way and two way classification