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