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 Research   >>   A Statistical Primer

Prof. Umasankar Mohanty, B.P.T, M.P.T (Manual Therapy), F.A.G.E

The present day health care delivery system believes in evidence-based practice. So a strong scientific temperament and research is necessary for any healthcare system for establishing the treatment methods. The field of physiotherapy has substantial scientific temperament. In order to establish a fact into a true science we rely on experimentation, data collection and statistical analysis. Research methodology and statistical components lends credibility, not only academically but professionally. It is important to understand research methods and statistics to evaluate other professionals research activities and reports as well as to put our own research and conclusions.  

Statistics is not a magic act. At its core, is the effort to understand variation. Statistics helps us to understand variation and its correlations. It facilitates us to derive some conclusion to our experimentation. In the article we put a birds eye view on the different statistical methods adapted to derive into some conclusions. In this overview I’ll provide some definitions of basic statistics terminology and attempt to provide a flow chart that helps to understand the type of information provided by some common statistical tests. I am by no means a statistician; my goal is for a conceptual understanding of the subject not mathematical.

Research is defined as a detailed study of a subject in order to discover (new) information or reach a (new) understanding. When engaged in research we must always end up in measuring something (muscle tone, pain assessment, functional improvements). These measurements are called as Data. There are two main ways of data presentation in research designs

  • Descriptive Statistics
  • Inferential statistics (a. Experimental designs b. Correlational designs).


  • Descriptive Statistics
  • Inferential statistics

The inferential statistics allow the researcher to make assumptions beyond the set of data in front of her/him.
The inferential statistics is presented with 2 designs a. Experimental designs b. Correlational designs

  1. Experimental design:

Attempts to define a cause and effect relationship through group comparisons. The experimental design is of following types:

  • True experimental design: Includes random assignment into experimental group (receives treatment) or control group (no treatment).
  •  Quasi-experimental designs: Lacks randomization, Control groups.
  • Within subject designs (repeated measures): Subjects serve as their own controls; randomly assigned to treatment or no treatment blocks.
  • Between subject designs: Comparisons made between groups of subjects.
  • Single-subject experimental design: Involves a sample of one with repeated measurements and design phases. It is of following types.

A-B design: Involves two phases, a pretreatment or baseline phase followed by an intervention or treatment phase.
A-B-A design: Multiple baseline design involving three phases (baseline phase, treatment phase, second baseline phase)
A-B-A-B design: Multiple baseline, Multiple treatment includes baseline, treatment, additional baseline and treatment phases.

  1. Correlational Designs

Retrospective - Investigation data collected in the past.
Prospective - Recording and investigation of present data.
Predictive - Useful to develop predictive models.
Attempts to determine whether a relationship exists between two or more quantifiable variable and to what degree.
Degree of relationship is expressed as correlational coefficient, ranging from –1.00 to +1.00.
If the correlation near +1.00, the variables are positively correlated.
If the correlation near 0.00, the variables are not related.
If the correlation near -1.00, the variables are inversely related.


  • Independent variable: The activity or factor believed to bring about a change in the dependent variable. The cause or treatment.
  • Dependent variable: The change or difference in behavior that results from the intervention (Independent variable); the outcome that is being evaluated.

A tentative and testable explanation of the relationship between variables; the results of an experiment determine if the hypothesis is accepted or rejected.

  • Directional hypothesis (research): A generalization that predicts an expected relationship between variables.
  • Null Hypothesis: states that no relationship exists between variables, a statistical hypothesis; any relationship found is the result of chance or sampling error. 


There are four levels of measurement. These levels are a hierarchy with nominal at the lower end and ratio at the top. As you move from higher to lower you lose information and have less ability to mathematically and statistically manipulate the data.

Nominal: Qualitative data with no natural ordering; Characteristics or attributes may be randomly coded numerically but the numbers really provide no information about the variable. For instance you might have the categories male and female and code them "1" and "2" respectively.

Ordinal: Qualitative data with an ordering. For instance if you were to measure ADL’s using a scoring system of 1=dependent, 2=max assist, 3=mod assist, 4=min assist, 5=independent.

Interval: Quantitative data in which there is a clear ordering and the distance between objects is specified but there is no meaningful zero point (absence of attribute). For instance temperature measured in Fahrenheit.

Ratio: Quantitative data which have classifies and ranks variables or scores based on equal intervals and a true zero point; the highest, most precise level of measurement; e.g. goniometry, scales for height, weight, or force allow the use of precise physical measures for research.


The selection of individuals (a sample) for a study from a population; the sample represents the largest group from which they were selected.

  • Random: All individuals in a population have an equal chance of being chosen for study.
  • Systematic: Individuals are selected from a population list by taking individuals at specified intervals, e.g. every 10th name.
  • Stratified: Individuals are selected from a population from identified subgroups based on some predetermined characteristics, e.g by height, weight or sex.
  • Double-blind study: An experiment in which the subject and the investigator are not aware of the group assignment.


For Descriptive Statistics
Measures of Central Tendency

Mode: The numeric value that occurs most frequently.
Median: The point on the numeric scale above which and below which 505 of the cases fall.
Mean: Sum of scores divided by total number of scores, arithmetic average.

Measures of Variability

Range: highest score minus the lowest score.
Standard deviation: used with interval or ratio level data, summarizes the average amount of deviation of all values of a distribution from the mean.
Variance: value of the standard deviation before a square root is taken. Variance is not typically reported in research but is often used in inferential statistical tests.

For Inferential Statistics

Allows the determination of how likely the results of a study of a sample can be generalized to the whole population.

  • Tests of significance: An estimation of true differences, not due to chance; a rejection of the null hypothesis.

Alpha level: Preselected level of statistical significance. Most commonly .05 or .01: indicates that the expected difference is due to chance, e.g at .05, only 5 times out of every 100 or a 5%chance, often expressed as a value of p.

Parametric vs. Nonparametric tests: Parametric tests require measurement on at least an interval scale and typically have a number of other assumptions regarding the distribution of variables. Parametric tests are measured with T-Test, Analysis of variance (ANOVA) and Analysis of covariance (ANCOVA). Nonparametric tests are applied to data collected on nominal or ordinal scales and have relatively far fewer assumptions. Non parametric tests are measured with Chi square test.

Answers to some frequently asked questions

How well does one variable predict another? Regression analysis
What is the degree that two variables are related?
Ratio / Interval data? Pearson Product Moment Correlation
Ordinal data? Spearman Rank Correlation
Is there a difference between/among group means?
Nominal data? Chi square
Ordinal data? Kruskal-Wallis One-way ANOVA by ranks (if less than 2 groups / comparisons) Wilcoxon Signed-Ranks test (more than 2 groups / comparisons, paired data)

Mann-Whitney U Test or Wilcoxon Rank Sum test (more than 2 groups / comparisons, unpaired data)
Ratio / Interval Data? T-Test (if only 2 groups / comparisons, may be done paired or unpaired)
ANOVA (if more than 2 groups / comparisons)


Assumption / Requirements

What will it tell me


  Ratio/Interval Data
  Paired Or Unpaired Data
  2 Groups To Be Compared

  Is There A Difference Between   Group Means


  Ratio/Interval Data
  Comparison Among >3 Group Means
  Paired Or Unpaired Data
  Repeated Measures Possible

  Is There A Difference Among Group   Means?

  Bonferroni Test

  Following ANOVA Within Subjects, Between   Subjects or Mixed Design

  Where Did Differences Occur   Among Group Means?

  Scheffe Test

  Following ANOVA (Post Hoc) Within Or Between   Subjects Design

  Where Did Differences Occur   Among Group Means?

  Tukey Test

  Following ANOVA (Post Hoc) Within Or Between   Subjects Design

  Where Did Differences Occur   Among Group Means?

  Dunnett Test

  Following ANOVA (Post Hoc) Within Or Between   Subjects Design Only To 1 Group Mean

  Where Did Differences Occur   Among Group Means?

  Linear Regression Analysis

  Ratio/Interval Data
  Homogeneity Of Variance

  Can I Predict One Variable Based   On Another

  Pearson Product Moment   Correlation

  Ratio/Interval Data
  Linear Relationship

  What Is The Degree Of Relationship   Between Two Variables?

  Spearman Rank Correlation

  Ratio/Interval Data
  Linear Relationship

  What Is The Degree Of Relationship   Between Two Variables?

  Chi Square

  Nominal/Ordinal Data

  Is The Distribution Of Observed   Frequencies Different From The   Expected Frequencies?


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  • Robson C 1974 Experiment, design and statistics in Psychology. Penguin, harmondsworth.
  • Iman Ronald 1994 A Data-Based Approach to Statistics, Duxbury Press.
  • Cobb George W 1997 Introduction to Design and Analysis of Experiments, Springer.
  • Moore David & McCabe George 1999 Introduction to the Practice of Statistics, 3rd ed. W.H. Freeman
  • Peck Roxy, Olsen Chris, Devore Jay 2001. The Introduction to Statistics and Data Analysis. Duxbury
  • Siegel Andrew, Morgan Charles 1996 Statistics and Data Analysis, 2nd ed. Wiley
  • Moore David,. 1996 Statistics: Concepts and Controversies. 4th ed W. H Freeman
  • Devore Jay, Peck Roxy 1993 Statistics: The Exploration and Analysis of Data Duxbury Press
  • Green J, D’ Oliveira M 1982 Learning to use statistical tests in psychology. Open University Press, Milton Keynes
  • Hicks Carolyn M. 1995 Research for Physiotherapists Project design and analysis. Churchill Livingstone

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