A descriptive statistic is a summary statistic. This presentation slides describes the descriptive statistics and its importance.

1. K.THIYAGU,
Assistant Professor,
Department of Education,
Central University of Kerala, Kasaragod
Descriptive Statistics

2. When
summarizing
quantitative
(Continuous/Interval/Ratio)
variables,
We are typically interested
in asking 4 questions like:

3. What is the
"center"
of the data?
Mean & Median

4. Measures of Central Tendency
•The average value of the distribution
Mean
•The middle value of the distribution
Median
•The most frequently occurring value
Mode

6. How spread out
is the data?
QD & SD

7. What are the
extremes of the data?
Minimum,
Maximum;
Outliers

8. Measures of Variability
• The
Range
• The
Average Deviation
• The
Standard Deviation
• The
Quartile Deviation

10. What is the "shape" of the distribution?
Is it symmetric or asymmetric?
Skewness, Kurtosis

11. Skewness
Right Skewed:
Skewness > +1.0
Normal Probability Curve
Skewness = -1 to +1
Left Skewed:
Skewness < -1.0
Kurtosis
Leptokurtic:
Kurtosis > +1.0
Mesokurtic:
Kurtosis = -1 to +1
Platykurtic:
Kurtosis < -1.0
Measures of the shape of the distribution
Interpretation for the Psychometric Purposes
A Skewness & kurtosis value of +/-1 is considered very good for most psychometric uses, but +/-2 is also usually acceptable.

12. Skewness

13. Kurtosis

14. Data Screening
Distribution Diagnosis
• Frequency tables
• Histograms and bar graphs
• Stem-and-leaf plots
• Box plots

15. Frequency
Tabulation
and
Percentage
are useful for
Categorical Data
Analyze
Descriptive
Statistics
Frequencies

17. Descriptive Statistics
SPSS
N valid responses
Mean
Sum
Standard deviation
Variance
Minimum
Maximum
Range
Standard Error of the mean
Skewness
Kurtosis

18. • This is the number of non-missing valuesValid N (listwise)
• This is the number of valid observations for the variable.N
• Minimum, or Smallest, value of the variable.Minimum
• Maximum, or Largest, value of the variable.Maximum
• MaximumMaximum
• Average of the observations (CT)Mean
• Square root of the variance. It measures the spread of a set of observations.SD
• It is the sum of the squared distances of data value from the mean divided by
the variance divisor.Variance
• Skewness measures the degree and direction of asymmetry. NPC = Skewness
= 0Skewness
• Kurtosis is a measure of tail extremity reflecting either the presence of outliers
in a distribution or a distribution’s propensity for producing outliersKurtosis

19. Normality Plots
&
Tests

20. Tests of Normality
•Claim:
•H0: The data come from the specified distribution;
•H1: The data do not come from the specified distribution
•It technically can be used to test if the data come from a known,
specific distribution (not just the normal distribution).
Kolmogorov-
Smirnov (K-S)
(Non-Parametric Test)
•Claim:
•Ho: The sample was drawn from a normal distribution.
•H1: The sample was not drawn from a normal distribution
Shapiro-Wilk
(Parametric Test)
The Shapiro-Wilk Test is more appropriate for small sample sizes
(< 50 samples), but can also handle sample sizes as large as 2000.

21. If p < Significant Level of Alpha ()
Or p < 0.05 / 0.01
Reject the null hypothesis.
There is sufficient evidence
that the data is not normally
distributed.
If p > Significant Level of Alpha ()
Or p > 0.05 / 0.01
Do not reject the null
hypothesis.
There is not enough evidence
to conclude that the data is
non-normal.
Tests of Normality
Criteria to Reject or Not Reject the Null Hypothesis:

22. Running the Procedure - SPSS
Analyze
Descriptive
Statistics
Explore
Add Variables
•Dependent List
box
Plots
•Normality plots
with tests.
•Continue.
Options
•Exclude cases
pairwise.
•Continue

23. Normal Q-Q Plot
In order to determine normality
graphically, we can use the output of a
normal Q-Q Plot. If the data are
normally distributed, the data points
will be close to the diagonal line

28. Median (Q2/50th Percentile):
The middle value of the dataset.
First Quartile (Q1/25th Percentile):
The middle number between the
smallest number (not the “minimum”)
and the median of the dataset.
Third quartile (Q3/75th Percentile):
The middle value between the median
and the highest value (not the
“maximum”) of the dataset.
Interquartile Range (IQR):
25th to the 75th percentile.
whiskers (shown in blue)
outliers (shown as green circles)
“Maximum”: Q3 + 1.5*IQR
“Minimum”: Q1 -1.5*IQR

30. Tooltip Description Procedure
Open data document Open a datafile File > Open > Data.
Save this document Save the active dataset File > Save or Ctrl + S.
Print Print the contents File > Print.
Undo Back to Previous Edit > Undo or Ctrl + Z.
Redo Equivalent to Edit > Redo or Ctrl + Y.
Go to case Jump to a specific case (row) Edit > Go to Case
Go to variable Jump to a specific variable (column) Edit > Go to Variable.
Variables View the variable name etc. Utilities > Variables.
Find Search for a value in the dataset Ctrl + F
Replace Replace a value in the dataset. Ctrl + H,
Insert cases Insert a case between two existing cases. Edit > Insert Cases.
Insert variable Insert a new variable between two existing variables Edit > Insert Variable.
Split file Stratify your analyses based on a categorical variable Data > Split File.
Select cases
Extract a set of cases to a new datafile based on some
criteria, or apply a filter variable.
Data > Select Cases.
Value labels
Toggle whether the raw data or the value label is
displayed in the Data View window
View > Value Labels.

33. Learn
Relearn
Unlearn

34. Thank you