it will help you better understanding the statistics in research

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)