Statistics in NursingStatistics in NursingResearch Research

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▫ Statistics is the science of making effective use of numerical  data which is related to collection, analysis and  interpretation of data.

Statistics is the study of how to collect, organizes, analyze, and Interpret data.  

DEFINITION DEFINITION

IMPORTANCE IMPORTANCE •  Statistics plays a vitally important role in the research.•  It help to answer important research questions and field in study.•  Helps you understand how to apply statistical method•  Important to understand what  tools are suitable for a particular       research study.•  Statistics enables to understand specified statistical concepts     and  procedures.

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TYPES OF STATISTICSTYPES OF STATISTICS

There are two approaches to the statistical analysis of data 1. Descriptive Statistics 1. Descriptive Statistics 

Descriptive statistics are techniques which help the investigator to organize, summarize and describe measures of a sample.  

2. Inferential statistics2. Inferential statisticsThe inferential approach helps to decide whether the outcome    of the study is a result of factors planned within design of the study or determined by chance.

                                                               (Streiner & Norman, 1996).

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FREQUENCY DISTRIBUTIONSFREQUENCY DISTRIBUTIONS

Frequency distribution is a systematic arrangement of values from lowest to highest or a method of organizing numeric data

22 23 2523 16 2015 24 2324 23 1623 18 2220 25 25

No.s (x) Frequency (f)

15 l

16 ll

18 l

20 ll

22 ll

23 llll

24 ll

25 lll18 Σ f =

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PRESENTATION OF DATA & PRESENTATION OF DATA & SHAPES SHAPES ▫ Tabular presentation▫ Diagrammatic Presentation▫ Graphical Presentation

A. Tabular Presentation of Data▫ Arranging values in columns is called tabulation.▫ E.g. The amount of oxygen content in water samples

B.  Diagrammatic Presentation of data▫ It is a visual form of presentation of statistical data in which data are

presented in the form of diagrams such as bars, lines, circles, maps▫ Common Types▫ Line Diagram▫ Pie diagram▫ Bar diagram

c. Line diagram 

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SHAPES OFSHAPES OF FREQUENCY DISTRIBUTIONFREQUENCY DISTRIBUTION

2. Polygons: polygonsuse dots connected by straight

lines to show frequencies.

1. Histograms: A histogram is constructed by drawing bars

Distribution are shown in Graphically. Graphs denotes the information of complete data in different shapes

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3. Symmetric distribution (Normal ) It consist of two halves that are mirror images of one another.

4. Asymmetric or Skewed distribution

It is off center and one tail is longer than the other

If the tail points to the left, the distribution is negatively skewed,

-When the longer tail points to the right, the distribution is positively skewed. 

A distribution with the modal peak off to one side or the other is described as skewed. The word skew literally means "slanted."

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5. Unimodal distribution It has only one peak or high point 

• (i.e., a value with small / high frequency),

6. Multimodal distribution It has two or more peaks

(i.e., values of high frequency).

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STATISTICS & DATA ANALYSIS STATISTICS & DATA ANALYSIS

Measures of central tendencyMeanModeMedian

Measures of variabilityRangeStandard deviationCorrelation

Inferential statisticsT- testChi square testANOVA

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CENTRAL TENDENCYCENTRAL TENDENCYIt is a statistical measure that identifies a single

score as representative for an entire distribution or group.

1. Mean2. Mode3. Median

Levels of measure used:Interval level variables - Mean Nominal variables - Mode Ordinal variables - Median

Measures of Central TendencyMeasures of Central Tendency

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1. Mean 1. Mean

• The mean (or average) is adding all the numbers and then divided by the number of observations in the data set. 

Example:        3,4,5,6,7 ▫ 3+4+5+6+7= 25,  25  N=5   The mean = 5

Exercise 1. Exercise 1. What is the average of these numbers?

567, 432, 902, 693, 356, 996

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2. Mode2. Mode

The mode in a set of data is the number that occurs

the most. E.g 25 10 10 25 5 10 25 10 5

Exercise 2: Find the mode of these numbers.

100 95 100 90 75 100 85 95 3. 3. MedianMedian

The median is a set of data , which is the middle number. Also arrange all the data from lowest to highest and then take the middle number.

E.g : odd : 3, 5, 8, 10, 11 median=8even: 3, 3, 4, 5, 7, 8

median=(4+5)/2=4.5

Exercise 3: Find the median 1. 67 34 85 33 84 & 2. 12 14 16 18 19 20

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Relationship between mean, median, and

mode is determined by the shape of the

distribution

CENTRAL TENDENCY AND THE SHAPE OF CENTRAL TENDENCY AND THE SHAPE OF THE THE DISTRIBUTIONDISTRIBUTION

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Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together.

If data has two distributions (Bivariante) with the same mean known as variability and have different shapes.

VARIABILITY (Disperson)VARIABILITY (Disperson)

Measure of variability or Measure of variability or DispersonDisperson

RangeStandard deviationCorrelation & co-efficient

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Range Range It is the difference between the lowest and highest

number in the set. Range = Xhighest – Xlowest

E.g: SAT scores of students at two nursing schools. Both distributionshave a mean of 500, but the score patterns are different. School A has a wide range of scores, with some below 300 and some above 700. This school has many students who performed among the best also many students who scored well below average. In school B, there are few students at either extreme.

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STANDARD DEVIATIONSTANDARD DEVIATION

Standard deviation is the most common measure of variability. It  is used the mean as a reference point  and  approximates the average distance of each score from the mean.

• A deviation (x) is the difference between an individual score and the mean. 

•VARIANCEVARIANCE▫The variance is simply the value of the standard deviation before a square root has been taken

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Formulas of standard DeviationFormulas of standard DeviationStandard Deviation (s or SD)* is

- 1st column is mean (X) = 7 - 2nd column = (X - X )- 3rd column each score is squared

( X – X )2

.

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CORRELATIONCorrelation is a measure of association between two 

variables.  Correlations can be graphed on scatter plot or scatter diagram

Scatter plot: Scatter plot: It involves making a rectangular coordinate graph with the two variables laid out at right angles. plot (dots) are shown to help identify subjects.

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Positive Correlations : If the dots begins at the lower left corner and extends to the upper right corner, the relationship is positive . Correlations fall between .00 and 1.00 are positive

Negative Correlations: Dots from the upper left corner to the lower right corner, the relationship is Negative. Correlations that fall between .00 and 1.00 are negative,

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CORRELATION COEFFICIENT CORRELATION COEFFICIENT (PEARSON’S – R)(PEARSON’S – R)

Correlation coefficients can be computed with two variables measured on either the ordinal, interval, or ratio scale

Pearson’s

Calculation…..VRV-India

INFERENTIAL STATISTICSINFERENTIAL STATISTICS

• Inferential statistics is a statistical method used to infer result s of sample (statistic) to population (parameter).

It is a process of inductive reasoning based on the mathematical theory of probability                                                             - (Fowler, J., Jarvis, P. -2002).

• Component of inferential statistics.▫Hypothesis testing▫Estimation 

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Error and Hypothesis testingThe standard deviation of a sampling distribution of

mean is called the Standard Error of the Mean (SEM). Error various means in the sampling distribution have some

error as estimates of the population meanSEM (symbolized as Sx)

If we use this formula to calculate the SEM for an SD of 100 with a sample of 25 students we obtain

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Errors Reject H0 Don't reject

H0

Truth

H0Type I Error

Right decision

H1Right decision

Type II Error

Type I error ()Accepting the experimental hypothesis when the null hypothesis is true

Type II error ()Accepting the null hypothesis when the experimental hypothesis is true

Conti…..Conti…..

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Hypothesis testing

• A study was conducted to determine the difference of knowledge score of hypertension between male and female adults in Bandar A. the result revealed t statistic 2.678, df 99, P value was 0.009(level of significance set at 0.05) and mean difference 1.14

• Hypothesis▫ HO: there is no difference of knowledge score of hypertension

between male and female adults in Bandar A▫ HA: there is the differences of knowledge score of hypertension between

male and female adults in Bandar A• Interpret the result

▫ P=0.009, α=0.05, p<α. Reject HO

• conclusion▫ There is difference of knowledge score of hypertension between male and

female adults in Bandar A

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ESTIMATIONESTIMATION

It is used to estimate a single parameter, like a mean. Estimation can take in to two forms.

Forms: Point estimation : Point estimation involves

calculating a single statistic to estimate the population parameter. Point estimates convey no information about accuracy

Interval estimation : it indicates a range of values within which the parameter has a specified probability of lying

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STATISTICAL TESTSSTATISTICAL TESTS

There are two types of inferential statistics1. Parametric 2. Non-parametric Tests

1. Parametric TestsA parametric test is one which specifies certain conditions 

about the parameter of the population from which a sample is taken.               E.g    t-test, and F-test (ANOVA)

2. Non-parametric tests (Distribution-free Statistics)A non-parametric test is one does not specify any conditions 

about the parameter of the population from which the population is drawn. These tests are called.  

E.g    Chi-squire test

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T- TEST T- TEST (Student’s t).

• It is used to testing the differences in group s of mean• t-test can be used when there are two independent groups 

(e.g., experimental versus control, male versus female),Degree of freedom (df)Degree of freedom (df)• Degree of freedom (df) is describes the number of events or observations that are free to vary. 

    Formula  Formula  t-Test Degrees of freedom (df)

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Example:Example:Maternity patients on perceived maternal competence.

We administer a scale of perceived maternal competence at discharge to 10 primiparas who remained in the hospital 48 to 72 hours (group A, regular discharge) and to 10 primiparas discharged less than 48 hours after delivery (group B, early discharge). The mean scale scores for these two groups are 25.0 and 19.0,

nA = 10 number of subjects in group AnB =10 number of subjects in group B

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Degrees of freedom :

df = [(10 + 10) - 2] = 18VRV-India

THE CHI-SQUARE TEST THE CHI-SQUARE TEST (Analyzing Frequencies)

The chi-squire test is used when the data are expressed in terms of frequencies of proportions or percentages.

The chi-square statistic is computed by comparing observed frequencies and expected frequencies

FORMULASFORMULASChi-square

Degrees of freedom (df) = [(R 1)(C 1)].

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Analysis of variance (ANOVA)Analysis of variance (ANOVA)

It is another commonly used parametric procedure for testing differences between means where there are three or more groups.The statistic computed in an ANOVA is the F-ratio , variation within groups to get an F-ratio.

TypesTypesOne way Anova, two way ANOVA, multifactor

ANOVA

FormulasFormulas

Calculation…..

MEAN SQUARE (MS) F- Ratio

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TYPES of ANOVATYPES of ANOVA

• One-way ANOVA ▫ It is used with one independent variable and one dependent variable).

• Two-way ANOVA or Factorial Analysis of Variance▫ Factorial analysis of variance permits the investigator to analyze the effects of two or more independent variables on the dependent variable.

• Analysis of Covariance (ANCOVA)▫ It is an inferential statistical test that enables investigators t adjusts statistically for group differences that may interfere with obtaining results that relate specifically to the effects of the independent variable(s) on the dependent variable(s).

• Multivariate Analysis▫ Multivariate analysis refers to a group of inferential statistical tests that enable the investigator to examine multiple variables simultaneously. 

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