presentation on statistics for research
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Lecture 7. Presentation on Statistics for Research. Contents. What is Statistics?- its scope Is Statistics Science or Arts?- Debatable Types of Data Presentation of Data Measure of Central Tendency Measures of Variability Chi square test T test for testing difference between two means. - PowerPoint PPT PresentationTRANSCRIPT
Presentation on Statistics for
Research
Lecture 7
Contents
What is Statistics?- its scope Is Statistics Science or Arts?- Debatable Types of Data Presentation of Data Measure of Central Tendency Measures of Variability Chi square test T test for testing difference between
two means
What is Statistics?
”Statistics is a body of methods or tools for obtaining knowledge”
That is Statistics is a tool for obtaining knowledge.
Example : correlation coefficient between height and weight is + 8.5
Functions of statistics:
•presents facts in definite form
•Simplifies huge number of figures and facilitates analysis
•Helps in formulating and testing hypothesis• helps in prediction
.
Scope of Statistics:
Vast, unlimited and ever increasing in
e.g. Biostatistics, Industrial statistics, Informatics, Design of experiments in agricultural production, Demography, Queuing Theory, Stochastic Process, psychology, sociology, public administration etc.
Types of Data
There are three types of data mainly:
1. Cross Sectional, 2. Time Series and3. Panel data
Cross Sectional Data:Cross-sectional data refer to observations of many individuals (subjects, objects) at a given time.
Example:Gross annual income for each of 1000 randomly chosen households in Dhaka City for the year 2009
Time series data Data:
Time series data also called Longitudinal data refer to observations of a given unit made over time.
Example of Time series data
Average gross annual income of, say, 1000 households randomly chosen from Dhaka City for 10 years 1991-2000.
Panel Data:
A panel data set refers contains observations on a number of units (e.g. subjects, objects) over time. Thus, panel data has characteristics of both time series and cross-sectional data .
Example of Panel data
Values of the gross annual income for each of 1000 randomly chosen households in Dhaka City collected for each of 10 years from 1991 to 2000. Such data can be represented as a set of double-indexed values {Vij; i=1,...,10, j=1,...,1000} .
Presentation of data
Pie chart, Bar chart and Column chart
export quantity by products of year 2010
Series1, 125, 8%
Series1, 800, 55%
Series1, 325, 22%
Series1, 225, 15%
tea
RMG
Jute
others
export quantity
125
800
325
225
0 500 1000
tea
RMG
Jute
others
export quantity
export of 2010
0
500
1000
tea RMG Jute others
products
qu
anti
ty
Series1
Pie chart Example
export value by products of year 2010
8%
55%
22%
15%
tea
RMG
Jute
others
Bar chart Example Projected export value in crore dollar
125
800
325
225
0 500 1000
tea
RMG
Jute
others
export quantity
Column chart Example
Projected export
0
500
1000
tea RMG Jute others
products
Series1
MEASURES OF CENTRAL TENDENCY
What is Measures of Central Tendency?Measures of Central Tendency are -
Mean, Median, Mode, Quartile, Percentile calculations
Measures of Central Tendency
Mean: For a population or a sample, the mean is
the arithmetic average of all values.
The mean is a measure of central tendency.
e.g. mean age of CSC students is say 38
The mean, symbolized by X, is the sum of the weights of students divided by the number of students whose weights have been taken.
The following formula both defines and describes the procedure for finding the mean
= X1 + X2 + X3 / 3
32,35,36,36, 37,38,38,39,39,39,40,40,42,45
Then the mean denoted as :
Median:
The median, symbolized by Md, is the value which lies in the middle point of the distribution so that half the values are above the median and half of the values are below the median.
Computation of the median is relatively straightforward
.
The first step is to serially write the values (called rank order of the values) from lowest to highest.
Then the Median is simply the middle number. In the case below, the Median would be 38 because there are 15
values all together with 7 values larger and 7 values smaller than the median.
32 32 35 36 36 37 38
38
39 39 39 40 40 45 46
Median in case of even number of values
Median is calculated as mid-point of the two middle numbers.38 + 39 / 2 = 38.5
32 35 36 36 37 38
38 39
39 39 40 40 42 45
Mode: Mode is a value that occurs most in a population or a sample. It could be considered as the single value most typical of all the values.
Example: For a set of numbers 1,2,3,7,3,8,9,5,3,8,9
the mode is 3 which occurs most
NB. Some population may have more than one mode and could be bi-modal.
Measures of Variability Variability refers to the spread or dispersion of
values scores.
A distribution of scores is said to be highly variable
if the scores differ widely from one another. There are Three measures of dispersion Range Variance Standard Deviation
Range Range is the difference between the largest value and smallest value. Range= Highest value-lowest value Distribution 1: 32 35 36 36 37 38 40 42 42 43 43 45
Distribution 2: 32 32 33 33 33 34 34 34 34 34 35 45
Although the range is (45-32) 13 for both the distribution but doesn’t give true picture about the variability.
Measures of Variability (Variance and Standard Deviation)
: The variance, symbolized by "s2", is a measure of variability.
The standard deviation, symbolized by "s", is the positive square root of the variance.
2S
Formula of Standard Deviation
Standard Deviation is the positive Square root of Variance 2
1
)(
N
XXiS
Example of Variance and Standard Deviation
Series 1 : 32 36 37 37 38 40 42 42 43 43 45 45
Mean X = 480/12 = 40Student No.
12 3 4 5 6 7 8 9 10 11 12
Weights of students
32
36 37 37 38 40 42 42 43 43 45 45
Xi - X
-8
-4 -3 -3 -2 0 2 2 3 3 5 5
(Xi –X) 2 6416 9 9 4 0 4 4 9 9 25 25
Sum of squares = 186
Therefore Variance S2=186 / n-1 = 186 /11 = 16.9
Standard Deviation = 4.11
Means average variation of the series from the mean value is 4.11
Chi Square Test
Tests difference in qualitative values For example, whether people have a definite
taste for colored cars compared to white cars Suppose in Bangladesh 1000 cars are sold in a month. If there was no preference for colored cars,
then:
Chi square TestTypes of Colors
Observed no.(O)
Expected no.(E)
O-E (O-E)**2 (O-E)**2/E
White 400 500 -100 10000 20
Colored 600 500 100 10000 20
Total = 40
From Chi-square table, find value for n-1 = 2-1=1 degree of freedom.
Reject null hypothesis if Calculated Value greater than Tabulated value
The End