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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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Conti..
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
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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
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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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