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DIFF. BRANCHES OF STATISTICS 1) Medical Statistics 2) Health statistics 3) Vital statistics 4) Biostatistics
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STATISTICS
Meena Ganapathy
MEANINGS
tatisticsL
atin-statusI
talian statisticaG
ermany StatistikF
rench statistiqueS
tatistic – Singular- One value associated e.g., wt of one personP
lural e.g., wt of more valuesS
tatistics as singular branch of science- It is the combination of logic & Mathematics.
DIFF. BRANCHES OF STATISTICS
1) Medical Statistics
2) Health statistics
3) Vital statistics
4) Biostatistics
STATISTICS
It is the branch of Science which deals with technique of collection, compilation, presentation, analysis of data & logical interpretation of the result.
USE OF STATISTICS
1.To collect the data in best possible way.
2.To describe the characteristics of a group or a situation.
3.To analyze data & to draw conclusion from such analysis.
DEFINITIONV
ariable :- A characteristic that take different values in different person places or things.E
.g. Ht, Wt, B.P., Age;’I
t is denoted by capital x = xE
.g., x: htX
1, x2, x3, x4…….xn
N= total numbers of observation
ATTRIBUTE
A qualitative characteristic like age, sex, nationality is called as attribute
CONSTANT
The characteristic which does not change its value or nature is considered as constant
E.g. blood group, sex
OBSERVATION
An event or its measurement such as BP., Is as event & 120/80 mm of Hg. Is as measurement
OBSERVATION UNIT
The source that gives observation such as object person etc.
DATAA
set of values recorded on one or more observational unit is called as data. It gives numerical observation about observational unit.
e.g., HT, WT, Age.
= equal to
< Less than
> greater than
=< less that & equal to
=> greater than & equal to
≠ not equal to
∑ Summation
Short forms
A.M.- arithmetic mean
H.M.- harmonic mean
G.M.- Geometric mean
C.V.- Coefficient of variation
S.E.- Standard error
S.D.- Standard deviation
D.F.- Degree of freedom
C.I.- Confidence interval
E :- Expected value of cell of contingency table
O :- Observed value of cell of contingency table.
N :- Population size
N :- Sample size
L :- Level of significance (I.O.S)
H
o :- Null hypothesisH
1 Alternative hypothesis
TYPES OF DATA
Qualitative and quantitative
Discrete and continuous
Primary and Secondary
Grouped and ungrouped
QUALITATIVE & QUANTITATIVE DATA
Qualitative data :-It is also called as enumeration data. It represents particular quality or attribute there is no notion of measurement. It can be classified by counting individuals having the same characteristics.
E.g. Sex, religion, blood group
QUANTITATIVE DATA
It is also called as measurement data. This can be measures by counting the characteristics in the variable.
E.g. Ht, Wt, BP, HB
DISCRETE & CONTINUOUS
Discrete :- Here we always get a whole number.
E.g. no of people dying in road accidents no. of vials of polio vaccine.
Continuous :- In this data there is possibility of getting fraction like 1.2, 2.1,3.81. i.e. it takes all possible values in a certain range.
E.g., Ht, WT, temp
PRIMARY AND SECONDARY
Primary :- The data obtained directly from a individual gives precise information. i.e., when the data is collected originally by the investigator for the first time is called primary data.
E.g. to find no. of alcoholic person in Karvenagar area. By the investigator.
Secondary :- When the data collected by somebody or other person is used the data is called secondary data.
E.g. Census hospital records
UNGROUPED AND GROUPED
Ungrouped :- When the data is presented in raw way , it is called as ungrouped data
E.g. Marks of 5 students
20,30,25,20,30
Grouped :- When the ungrouped data is arranged according to groups, then it is called as grouped data.
E.g. Marks Students
20 2
30 2
25 1
METHODS OF DATA COLLECTION
Observation Visual
Instrument
Instrument Properties
Reliability Validity
Interviews & self administered questionnaires
Use of documentary sources (secondary data)
CLASSIFICATION OF DATA
Definition :- The process of arranging data in to groups or classes according to similar characteristics is called as classification & the group so formed are called as class limits 1 class interval.
OBJECTIVES OF CLASSIFICATION OF DATA
1.It condense the data
2.It omits unnecessary information.
3.It reveals the important features of the data.
4.It facilities comparison with other data
5.It enables further analysis like competition of average, dispersion (Variables ) data.
FREQUENCY
A) Frequency
Definition :- No. of times variable value is repeated is called as frequency.
B) Cumulative class frequency
Definition :-Cumulative frequency is formed by adding frequency of each class to the total frequency at the previous class. It indicates the no. of observations < upper limit of the class limit.
Representatives Symbol
Sample Population
1. Mean X bar M
2. SD $ o 2
3. Variance $2 o2
4. Proportion p P
5. Complement of
proportion 2 Q
DATA PRESENTATION
Meena Ganapathy
METHODS OF PRESENTATION OF DATA
Tabulation.
Charts and diagrams.
METHODS OF PRESENTATION OF DATA
Caption headingStubheading
Caption
SubheadingTotal
S TUB
Total
Body of theTable
IMPORTANT POINTS IN MAKING A TABLE
Table No. :- If many tables are present
Title :- Should be small
Head note :- Whatever is not covered in title can be written in head note.
E.g. expressing units
Caption :- column heading
According to characteristics
Stub :- raw
Subheading
Body :- content
Foot note:- Short forms or
Source note :- resource it is important because it shows reliability of table.
RULES AND GUIDELINES FORTABULAR PRESENTATION
1. Table must be numbered
2. Brief & self explanatory title must be given to each table.
3.The headings of columns & rows must be clear, sufficient, concise & fully defined.
4. The data must be presented according to size or importance chronologically alphabetically or geographically.
5. Table should not be large.
6. Foot note should be given whenever necessary providing additional information sources or explanatory notes.
TYPES OF TABLE
1.One way table/simple table
2.Two way table
3.Complex table
1.ONE WAY TABLE/ SIMPLE TABLE
When there is only one characteristics is described in a table then it is called as simple table
EXAMPLE OF ONE WAY TABLE
Class interval Frequency
Tally Mark Frequency
3 – 4 IIII 5
5 - 6 II 2
7 – 8 IIII 5
9 - 10 III 3
TWO WAY TABLE
In this table data is classified according to two characteristics it given information about two interrelated characteristics.
Frequency distribution table qualitative data distribution of types of anemia
According to sex
Sex Types of anemia Total
Boys
160 85 15 260
Girls 190 120 45 355
Total
350 205 60 615
COMPLEX TABLE
Information collected regarding 3 or 4 characteristics & tabulated according to these characteristics such a type of table is called as complex table.
EXAMPLE OF COMPLEX TABLE
Fasting blood Male Female Total
Glucose 51-60 & 61-70yrs 51-60 & 61-70 yrs 120-129 4 4 2 2 12
130-139 1 3 3 1 8
140-149 2 4 1 3 10
150-159 2 3 3 2 10
160-169 4 5 3 3 15
170-179 5 4 5 4 18
180-189 1 2 1 1 5
19 25 18 16 78
ADVANTAGES OF A GRAPHS & DIAGRAMS
1. Information is presented in condensed form
2. Facts are presented in more effective & impressive manner as compared to tables
Easy to understand for a layman.
Create effect which last for longer time
Facilitate the comparison.
Help in revealing patterns.
DISADVANTAGES
Approximate results instead of accuracy
Gives only a general idea
Not sufficient for statistical analysis
TYPES OF DIAGRAMS FOR QUALITATIVE DATA
Bar: Simple, Multiple or complex, Component & Proportional
Pie or Sector
Pictograms
Shaded Map / Contour / Spot Maps
BAR DIAGRAMS
It is used to compare variables possessed by one or more groups.
SIMPLE BAR DIAGRAM
Here only one variable is presented
Bars are at uniform distance from one another
It can be drawn vertically or horizontally
Each should have title & source note
No. of dependents at home
1721
34
47
97103
0
20
40
60
80
100
120
None 1 2 3 4 5 andabove No. of dependents
No.
of s
ubje
cts
PIE OR SECTOR DIAGRAMS
When the data is presented as sum of different components for one qualitative characteristics we use pie diagrams.
Patients age distribution in percentage
21%
19%
26%
34%19-2930-3940-4950-59
PICTOGRAMS
This diagrams are useful for lay people. E.g., Village map indicating temple, trees etc…
SPOT MAPS
In this diagram a map of an area with location of each case of an illness, death etc… are identified with spots or dot or any other symbol.
TYPES OF DIAGRAMS FOR QUANTITATIVE DATA
Histograms
Frequency polygon
Frequency curve
Cumulative frequency curve
Line graph
Scatter diagram
Population Pyramid
Growth chart
HISTOGRAMSI
t is the graphical representation of frequency distribution. It is a series of adjacent rectangles erected on bars
Areas of these bars denote the frequency of respective class interval.
X axis base of bars shows class width of class interval
Y axis frequency / No of observations
0102030405060708090
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
EastWestNorth
FREQUENCY POLYGON
It is representation of categories of continuous & ordered data similar to histogram. It can be drawn in two ways: Using histograms, with out using histograms.
Uses: it is used when sets of data are illustrated on the same diagram such as temperature, & pulse, birth & death rate etc…
050
100150200250300350
1 2 3 4 5 6 7
Series1
Series2
SCATTER DIAGRAMS
It is prepared after tabulation in which frequencies of two variables have been cross classified
It is graphic representation of co relation between two variables
SCATTER PLOT
0100200300400500600700
0 5 10 15
Series1
LINE DIAGRAMS
It is used to show the trends of events with the passage of time. E.g., rising & falling
LINE GRAPH
0100200300400500600700
1 2 3 4 5 6 7
Series1
Series2
LINE & BAR
02468
101214
1 2 3 4 5 6 70100200300400500600700
Series2
Series1
MEASURES OF CENTRAL TENDENCY
Mode-Value that occurs most frequently
Median –point below and above 50% of cases fall
Mean-mathematical average( sum of scores divided by the total # of scores
Level of measurement plays a role in which central tendency measure you
Mean-interval & Ratio
Mode-Nominal
Median-ordinal
VARIABILITY / CENTRAL DISPERSION
Extent to which scores deviate from each other
Homogenous
Heterogeneous
Range-highest score-lowest
Distance between high & low scores
Standard Deviation (SD)
Difference between individual score and mean
Weight of person A=150 lbs
Mean =140
Deviation =+10
SD ( average deviation from mean )
Formula
BIVARIATE STATISTICS
Associations between 2 variables
Correlations
INFERENTIAL STATISTIC
Hypothesis testing
Null Ho
No actual relationship between variables
There will be no difference in grant writing ability between nurses who attend and do not attend the research short course
Accept the null Ho
Reject the null Ho
Type I Error
Reject the null when it is actually true
Type II Error
Accepting the null when it is actually false
Level of significance
Probability of committing Type I Error
Set by the researcher
Usually set at p =.05
Lowering risk to Type I increases risk of Type II
PARAMETRIC TESTS
Involve estimation of at least one parameter
Interval level data / Ratio scale
Assume variables are normally distributed
NONPARAMETRIC TESTS
Nominal or ordinal level data
Less restrictions about distributions
Between subjects testing
Men versus women
Within subjects testing
Same group compared pre and post-intervention
DIFFERENCES BETWEEN 2 GROUP MEANS
Parametric
T-tests for independent groups
Paired t-Tests
Nonparametric
Mann Whitney U
Wilcoxon signed rank test
DIFFERENCES BETWEEN 3 OR MORE GROUP MEANS
Parametric
One-Way Analysis of Variance (ANOVA)
F ratio test
Post-hoc tests to see which groups differ from each other
LSD; Bonferroni
Multifactor ANOVA (MANOVA)
More than 2 IVs
Usually for more complex analyses
EG., Human behavior, feelings
Repeated Measures ANOVA
3 or more measures of same DV for each subject
EG., subjects exposed to 3 or more different treatment conditions
3 more data collection points of DV over time (longitudinal)
Nonparametric ‘analysis of variance’
Kruskal wallis
TESTING DIFFERENCES IN PROPORTIONS
DV is nominal level
Chi square test
RELATIONSHIPS BETWEEN 2 VARIABLES
Pearson’s (interval level)
Spearman’s rho or Kendall's tau
(ordinal)
POWER ANALYSIS
The probability of obtaining a significant result is called power of a statistical test
Insufficient power-greater risk of Type II error
4 components
Significance level-more stringent, lower the power
Sample Size-increases, power increases
Population effect size (gammaY)- how strong effect of IV is on the DV
P
ower (1-B)-probability of rejecting null Ho
MULTIVARIATE STATISTICS
Simple linear regression
Make predictions about phenomena
R-correlation
R2proportion of variance in Y accounted for by combined Xs
Analysis of Covariance (ANCOVA)
Tests significance of differences between group means after adjusting scores on DV to eliminate effects of covariate (s)
Anxiety pre and post biofeedback therapy
One hospital = treatment
One hospital = control
Post anxiety DV; hospital condition IV
Pre anxiety scores- covariate
Discriminant Analysis
Predicts group membership
Nurses who graduate versus drop outs
Cancer patients adhere to treatment versus those who don’t
Logistic Regression
Binomial Logistic Regression
DV is categorical (2 groups)
Odds of Belonging to one group
Multinomial Logistic Regression
DV is categorical (. 2 groups)
Odds of belong to one group