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Statistics in research by dr. sudhir sahu
- 1. Statistics in Research By- Dr. Sudhir Sahu
- 2. Meaning and Types of Data • Data is the things known or assumed; facts and figure from which conclusion can de inferred. • Data are the raw materials used to construct meaning in research. • Data are of two types • 1. Quantitative and 2. Qualitative
- 3. What is Meant by Statistics? Statistics is the science of organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions.
- 4. Quantitative Variables - Classifications Quantitative variables can be classified as either discrete or continuous. A. Discrete variables: can only assume certain values and there are usually “gaps” between values. EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc). B. Continuous variable can assume any value within a specified range. EXAMPLE: The pressure in a tire, the weight of a pork chop, or the height of students in a class.
- 5. Summary of Types of Variables
- 6. Scale of Measurement • Four type of Scale of Measurement • Nominal- Discreet, Dichotomous, Dichotomized variable • Example- Caste System- General, OBC, SC, ST • Ordinal- frequencies, position, rank, order • Example- High, average, Low. • Interval- Continuous series of data (Can measure Mean/Average) • Example- Marks, IQ, SES etc. • Ratio- Continuous series with true zero point • Example- Price, Materials etc.
- 7. Types of Statistics – Descriptive Statistics and Inferential Statistics Descriptive Statistics – -Methods of organizing, summarizing, and presenting data in an informative way. Descriptive values/ characteristics can measures through statistics EXAMPLE 1: The United States government reports the population of the United States was 179,323,000 in 1960; 203,302,000 in 1970; 226,542,000 in 1980; 248,709,000 in 1990, and 265,000,000 in 2000. EXAMPLE 2: According to the Bureau of Labor Statistics, the average hourly earnings of production workers was $17.90 for April 2008.
- 8. Types of Statistics – Descriptive Statistics and Inferential Statistics Inferential Statistics: A decision, estimate, prediction, or generalization about a population, based on a sample. Inferential values/ characteristics can measures through Parameter
- 9. Statistics Descriptive Central Tendency Mean Mode Median Measures of Dispersion Range MD SD Quartile Deviation Percentile NPC Inferential Parametric t-Test/ CR F-Test ANOVA - Two, Three, Four Way ANCOVA MANOVA MANCOVA Repeated- Measures r Non Parametric Sign Test Chi-Squares Rho phi- Correlation Bi-serial Point- Biserial
- 10. Descriptive Statistics • Central Tendency: • Mean: • Arithmetic Average of a distribution • Suitable for Continuous Variables on Interval or Ratio Scale Data • Median- • Middle most point of the distribution- • Suitable for Ordinal Scale of data • Mode- • Most numbers of times occurring of a score in a distribution • Suitable for Discreet and Nominal Data
- 11. Descriptive Statistics • Measures of Dispersion/ Variability- • Rank- • Distribution from highest to lowest scores. • Continuous series of data on more than interval- scale • Mean Deviation/ Median Deviation (MD): • Average of Deviation of each scores from the central value (Mean/Median) of the distribution • Suitable for Continuous series of data on more than interval- scale • Standard Difference (SD) • Square root of the sum of square of deviations calculated for each item. • Continuous series of data on more than interval- scale • Variance • Square of SD, generally used in Factorial analysis • Quartile Deviation- • One half of the distance between Q3 (P75) and Q1 (P25) Q3- Q4 (P75 –P100) Q2-Q3 (P25- P75) Q1-Q2 (P1- P25)
- 12. Descriptive Statistics • Measures of Relative Position • Percentile- • Percentiles are the point which distribute the entire distribution to 100 equals parts. • Percentile Rank- • Position of a score below which certain percentage of score (percentile) lies. • Standard Scores (Z scores or T Scores) • Conversion of Raw distribution or scores to a Standard Scores. • Stanine Scores- • Division of the entire distribution scores in to 10 equals parts.
- 13. Descriptive Statistics • Measures of Relative Position • Normal Probability Curve (NPC) • Distribution of scores from approximately -3 SD to +3 SD.
- 14. Inferential Statistics • Parametric- • Parameter is similar as mean for same so as here for the population. • Applicable for continuous series data with more than interval scale • t- Test • To compare Two groups on their mean. • Example-Male and Female on Achievement • F-Test • To compare more than two groups without their levels • Example- To compare General, OBC, SC and ST students on Adjustment • Also known as One-Way ANOVA
- 15. Inferential Statistics • ANOVA- (Univariate) • Two or more than two independent variables with their more than two levels. • Two –Way ANOVA- 2×2, 3×2, 3×3, etc • Three Way ANOVA- 2×2×2, 3×2×2, 2×2×3, 4×2×3 etc ANCOVA- (Univariate) • More than two independent variable with their levels • Try to Stabilized/Control effect of one independent variable on dependent variables. MANOVA- (Multi- Variate) • More than two independent variables with their levels on More than two dependent variables simultaneous • MANCOVA- • Control of one independent variable and analysis of the effect of other independent variables on more than two Dependent Variables. • Product Movement Correlation (r) – • Continuous series more than interval data (Discrete and Continous)
- 16. Inferential Statistics • Non- Parametric Test- • No parameter or mean based observation. • When the nature of the data is Discrete and in Nominal or Ordinal Scale this type of tests are effective in producing judgement. • Sign Test • Based on Nominal Scale and discrete data,. • Generally used Sign of Greater than and Smaller than (˂ or ˃) . • Chi-squares- • Comparison of various groups on the basis of frequencies obtained. • Suitable for ordinal scale and discrete variables. • Rank difference Correlation (Rho) • Suitable for ordinal scale data • Biserial Correlation • (Nominal/Ordinal) • Point-Biserial correlation • (Nominal/Nominal)