Computer Oriented Statistical Techniques Syllabus
The Mean, Median, Mode, and Other Measures of Central Tendency: Index, or Subscript, Notation, Summation Notation, Averages, or Measures of Central Tendency ,The Arithmetic Mean , The Weighted Arithmetic Mean ,Properties of the Arithmetic Mean, The Arithmetic Mean Computed from Grouped Data ,The Median ,The Mode, The Empirical Relation Between the Mean, Median, and Mode, The Geometric Mean G, The Harmonic Mean H ,The Relation Between the Arithmetic, Geometric, and Harmonic Means, The Root Mean Square, Quartiles, Deciles, and Percentiles, Software and Measures of Central Tendency.
The Standard Deviation and Other Measures of Dispersion: Dispersion, or Variation, The Range, The Mean Deviation, The Semi- Interquartile Range, The 10–90 Percentile Range, The Standard Deviation, The Variance, Short Methods for Computing the Standard Deviation, Properties of the Standard Deviation, Charlie’s Check, Sheppard’s Correction for Variance, Empirical Relations Between Measures of Dispersion, Absolute and Relative Dispersion; Coeﬃcient of Variation, Standardized Variable; Standard Scores, Software and Measures of Dispersion.
Introduction to R: Basic syntax, data types, variables, operators, control statements, R-functions, R –Vectors, R – lists, R Arrays.
Moments, Skewness, and Kurtosis: Moments , Moments for Grouped Data ,Relations Between Moments , Computation of Moments for Grouped Data, Charlie’s Check and Sheppard’s Corrections, Moments in Dimensionless Form, Skewness, Kurtosis, Population Moments, Skewness, and Kurtosis, Software Computation of Skewness and Kurtosis.
Elementary Probability Theory: Deﬁnitions of Probability, Conditional Probability; Independent and Dependent Events, Mutually Exclusive Events, Probability Distributions, Mathematical Expectation, Relation Between Population, Sample Mean, and Variance, Combinatorial Analysis, Combinations, Stirling’s Approximation to n!, Relation of Probability to Point Set Theory, Euler or Venn Diagrams and Probability.
Elementary Sampling Theory: Sampling Theory, Random Samples and Random Numbers, Sampling With and Without Replacement, Sampling Distributions, Sampling Distribution of Means, Sampling Distribution of Proportions, Sampling Distributions of Diﬀerences and Sums, Standard Errors, Software Demonstration of Elementary Sampling Theory.
Statistical Estimation Theory: Estimation of Parameters, Unbiased Estimates, Eﬃcient Estimates, Point Estimates and Interval Estimates; Their Reliability, Conﬁdence-Interval Estimates of Population Parameters, Probable Error.
Statistical Decision Theory: Statistical Decisions, Statistical Hypotheses, Tests of Hypotheses and Signiﬁcance, or Decision Rules, Type I and Type II Errors, Level of Signiﬁcance, Tests Involving Normal Distributions, Two-Tailed and One-Tailed Tests, Special Tests, Operating-Characteristic Curves; the Power of a Test, p-Values for Hypotheses Tests, Control Charts, Tests Involving Sample Diﬀerences, Tests Involving Binomial Distributions.
Statistics in R: mean, median, mode, Normal Distribution , Binomial Distribution, Frequency Distribution in R.
Small Sampling Theory: Small Samples, Student’s t Distribution, Conﬁdence Intervals, Tests of Hypotheses and Signiﬁcance, The Chi- Square Distribution, Conﬁdence Intervals for Sigma , Degrees of Freedom, The F Distribution.
The Chi-Square Test: Observed and Theoretical Frequencies, Deﬁnition of chi-square, Signiﬁcance Tests, The Chi-Square Test for Goodness of Fit, Contingency Tables, Yates’ Correction for Continuity, Simple Formulas for Computing chi-square, Coeﬃcient of Contingency, Correlation of Attributes, Additive Property of chi- square.
Curve Fitting and the Method of Least Squares: Relationship Between Variables, Curve Fitting, Equations of Approximating Curves, Freehand Method of Curve Fitting, The Straight Line, The Method of Least Squares, The Least-Squares Line, Nonlinear Relationships, The Least-Squares Parabola, Regression, Applications to Time Series, Problems Involving More Than Two Variables.
Correlation Theory: Correlation and Regression, Linear Correlation, Measures of Correlation, The Least-Squares Regression Lines, Standard Error of Estimate, Explained and Unexplained Variation, Coeﬃcient of Correlation, Remarks Concerning the Correlation Coeﬃcient, Product-Moment Formula for the Linear Correlation Coeﬃcient, Short Computational Formulas, Regression Lines and the Linear Correlation Coeﬃcient, Correlation of Time Series, Correlation of Attributes, Sampling Theory of Correlation, Sampling Theory of Regression.
Computer Oriented Statistical Techniques Practicals
|1||Using R execute the basic commands, array, list and frames.|
|2||Create a Matrix using R and Perform the operations addition, inverse, transpose and multiplication operations.|
|3||Using R Execute the statistical functions: mean, median, mode, quartiles, range, inter quartile range histogram|
|4||Using R Execute the statistical functions: mean, median, mode, quartiles, range, inter quartile range histogram|
|5||Using R import the data from Excel / .CSV file and Calculate the standard deviation, variance, co-variance.|
|6||Using R import the data from Excel / .CSV file and draw the skewness.|
|7||Import the data from Excel / .CSV and perform the hypothetical testing.|
|8||Import the data from Excel / .CSV and perform the Chi-squared Test.|
|9||Using R perform the binomial and normal distribution on the data|
|10||Perform the Linear Regression using R.|
|11||Compute the Least squares means using R.|
|12||Compute the Linear Least Square Regression|
Computer Oriented Statistical Techniques Reference Books
|Authors||Murray R. Spiegel, Larry J. Stephens.|
|Publisher||McGraw – Hill International|
|Title||A Practical Approach using R|
|Authors||R.B. Patil, H.J. Dand and R. Bhavsar|
|Title||Fundamental Of Mathematical Statistics|
|Authors||S.C. Gupta And V.K. Kapoor|
|Publisher||Sultan Chand And Sons|
|Authors||J.N. Kapur And H.C. Saxena|