Statistical Analysis: Descriptive and Inferential Techniques Overview

 
Descriptive and Inferential
Statistic
 
Dr. Dyal Bhatnagar
STATISTICS
 
Manipulating Data to get meaningful
inferences out of it.
‘Data’ is plural or singular?
Variables
 
Metric (Continuous)
 
Ratio Variable
Interval Variable
 
Non-Metric (Categorical)
 
Ordinal Variable
Nominal Variable
 
Values that look interval are often ordinal
     
- Andy Field
 
Continuous variables are continuous (obviously) but also discrete
Statistical Techniques
 
Descriptive Statistical Techniques
 
These techniques are used
to describe the basic
features or characteristics
of data under study
Measures of Central tendency
Measures of Dispersion
Measures of Skewness
Measures of Kurtosis
 
Inferential Statistical Techniques
 
Inferential statistics uses a
random sample of data
taken from a population to
make inferences about the
population
Finding relationship among
variables
Testing a hypothesis
Measures of Central Tendency
 
Mean: The average
Median: A point in data set that divides data
set in two equal halves
Mode: The most frequent value
 
Measures of Dispersion
Measures of Dispersion
 
Absolute Measures
 
The output is an absolute
value represented in the
same unit of measurement
as of the data
 
Relative Measures
 
Coefficient of an absolute
measure is calculated.
Coefficient is a pure number
independent of the unit of
measurement
 
 
Variance is the square of deviations from the
central value divided by the number of
observations
 
 
 = √V or V = 
2
 
 
 
Skewness and Kurtosis
 
The Dispersion tells about the 
extent
 of
variation in a distribution, where as, Skewness
tells about the 
direction 
of variation
Kurtosis tells if the distribution is peaked or
flat.
Correlation
 
Correlation measures the joint variation
among two or more variables.
Correlation does not mean there is causation,
but causation always implies correlation.
Negative and positive correlation
Linear and non-linear correlation
Simple, Partial or multiple correlation
Regression
 
Measuring cause and effect relationship
among two or more variables.
The direction of causation can be either from
X to Y or otherwise.
Y = 
 + 
X
 
Hypothesis Testing
 
1. Set up a Null Hypothesis
 
H
o 
 asserts that there is no real difference in
the samples or between the sample and the
population and difference found is arising out
of sampling fluctuations.
H
o
 
   
1
 = 
2
Status quo
We generally wish to reject the H
o
 
 
 
 
2. Set up a significance level (
)
 
Significance level indicates the probability of
rejecting the H
o 
 when it was true.
It is the risk of error the researcher is ready to
accept.
 
 
 
 
The only way to reduce the probability of errors is
to increase the sample size
3. Decide about the tails of test
 
A directional H
o 
 is tested using a one tailed
test and a non-directional H
o 
 is tested with a
two tailed test.
Directional H
o
 
   
1
2
Non-directional H
o
 
   
1
 = 
2
In case of two tail test the significance value
will be reduced to half
4. Choose a test
 
This involves choosing an appropriate distribution for a
particular test
 
 
 
 
 
 
 
Assumption for parametric tests
The distribution is normally distributed
Variance across samples is homogeneous
5. Run the test
 
6. Interpret the results
p-Value represents the probability of concluding
incorrectly that there is a difference in samples,
when no true difference exists.
p-value < 
 
 Reject 
H
o
p-value > 
 
 Accept 
H
o
As we wish to Reject H
o 
 in most cases, we search
for p-values < 
 (0.05)
A p-value of 0.07 would mean more risk then
tolerable level i.e. 0,05
 
Thank-you
 
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Understanding statistical analysis involves both descriptive and inferential techniques. Descriptive statistics focus on summarizing data, including measures of central tendency and dispersion. In contrast, inferential statistics use sample data to make inferences about populations and test hypotheses. Variables can be categorized as metric or non-metric, and measures of skewness and kurtosis provide insights into data distribution. This overview covers key concepts such as mean, median, mode, variance, skewness, and kurtosis essential for meaningful data analysis.


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  1. Descriptive and Inferential Statistic Dr. Dyal Bhatnagar

  2. STATISTICS Manipulating Data to get meaningful inferences out of it. Data is plural or singular?

  3. Variables Metric (Continuous) Ratio Variable Interval Variable Non-Metric (Categorical) Ordinal Variable Nominal Variable Values that look interval are often ordinal - Andy Field Continuous variables are continuous (obviously) but also discrete

  4. Statistical Techniques Descriptive Statistical Techniques These techniques are used to describe the basic features or characteristics of data under study Measures of Central tendency Measures of Dispersion Measures of Skewness Measures of Kurtosis Inferential Statistical Techniques Inferential statistics uses a random sample of data taken from a population to make inferences about the population Finding relationship among variables Testing a hypothesis

  5. Measures of Central Tendency Mean: The average Median: A point in data set that divides data set in two equal halves Mode: The most frequent value

  6. Measures of Dispersion Series A Series B Series C 100 102 10 100 104 6 100 97 480 100 98 3 100 =100 99 1 =100 =100

  7. Measures of Dispersion Absolute Measures Relative Measures The output is an absolute value represented in the same unit of measurement as of the data Coefficient of an absolute measure is calculated. Coefficient is a pure number independent of the unit of measurement

  8. Variance is the square of deviations from the central value divided by the number of observations = V or V = 2

  9. Skewness and Kurtosis The Dispersion tells about the extent of variation in a distribution, where as, Skewness tells about the direction of variation Kurtosis tells if the distribution is peaked or flat.

  10. Correlation Correlation measures the joint variation among two or more variables. Correlation does not mean there is causation, but causation always implies correlation. Negative and positive correlation Linear and non-linear correlation Simple, Partial or multiple correlation

  11. Regression Measuring cause and effect relationship among two or more variables. The direction of causation can be either from X to Y or otherwise. Y = + X

  12. Hypothesis Testing

  13. 1. Set up a Null Hypothesis Ho asserts that there is no real difference in the samples or between the sample and the population and difference found is arising out of sampling fluctuations. Ho 1 = 2 Status quo We generally wish to reject the Ho

  14. 2. Set up a significance level () Significance level indicates the probability of rejecting the Ho when it was true. It is the risk of error the researcher is ready to accept. Accept Ho - Right decision - Type II error ( ) Reject Ho - Type I error ( ) - Right decision Ho is true Ho is false The only way to reduce the probability of errors is to increase the sample size

  15. 3. Decide about the tails of test A directional Ho is tested using a one tailed test and a non-directional Ho is tested with a two tailed test. Directional Ho 1 Non-directional Ho 1 = In case of two tail test the significance value will be reduced to half 2 2

  16. 4. Choose a test This involves choosing an appropriate distribution for a particular test Parametric Tests Non Parametric tests Z Test Sign Test t-test (Independent samples) Mann Whitney Test t-test (Paired samples) Wilcoxon Test F test (ANOVA) Kruskal Wallis Test Assumption for parametric tests The distribution is normally distributed Variance across samples is homogeneous

  17. Dependent Variable Metric Non-Metric Discriminant Analysis Binary/Logistic regression Independent Variable(s) Metric Regression Hypothesis testing Non-Metric Chi-square Test

  18. 5. Run the test 6. Interpret the results p-Value represents the probability of concluding incorrectly that there is a difference in samples, when no true difference exists. p-value < Reject Ho p-value > Accept Ho As we wish to Reject Ho in most cases, we search for p-values < (0.05) A p-value of 0.07 would mean more risk then tolerable level i.e. 0,05

  19. Thank-you

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