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• Introduction
• Measurement
• Population, Variable, Sample
• Hypothesis
• Types of errors
• Statistical Power
• Sampling
• Descriptive Statistics
• Inferential statistics
• Parametric and Non-parametric Tests
• Appropriate Statistical tests
• Common Statistical tests
• Multivariate Analysis
• Choosing the appropriate test
• Computer Aided Analysis
• References & Bibliography

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Common Statistical Tests

Regression Analysis

Regression analysis is often used to predict the value of one variable given information about another variable. The procedure can describe how two continuous variables are related. Regression analysis is used to examine relationships among continuous variables and is most appropriate for data that can be plotted on a graph. Data are usually plotted, so that the independent variable is seen on the horizontal (x) axis and the dependent variable on the vertical (y) axis. The statistical procedure for regression analysis includes a test for the significance of the relationship between two variables. Given a significant relationship between two variables, knowledge of the value of the independent variable permits a prediction of the value of the dependent variable.

One-Way Analysis of Variance (ANOVA)

When there are three or more samples, and the data from each sample are thought to be distributed normally, analysis of variance (ANOVA) may be a technique of choice One-way analysis of variance is a parametric inferential statistical test that enables the investigators to compare two or more group means, which was developed by RF. Fisher. The reporting of the results includes the df, F value and the probability level. ANOVA is of two types: simple analysis of variance and complex analysis of variance or two-way analysis of variance. One-Way Analysis of Variance (ANOVA) is an extension of t-test, which permits the investigator to compare more than two means simultaneously.

Researchers studying two or more groups can use ANOVA to determine whether there are differences among the groups. For example, nurse investigators who want to assess the levels of helplessness among three groups of patients--long-term, acute care and outpatients-can administer an instrument designed to measure levels of helplessness and then calculate an F ratio. If the F ratio is sufficiently large, then conclusion can be that there is a difference between at least two of the means can be drawn.

The larger the F-ratio, the more likely it is that the null hypothesis can be rejected. Other tests called post hoc comparisons, can be used to determine which of the means differ significantly. Fisher’s LSD, Duncan’s new multiple range test, the Neuman-Keuls, Tukey’s HSD, and Scheffe’s test are the post hoc comparison tests that are most frequently used following ANOVA. In some instances a post hoc comparison is not necessary because the means of the groups under consideration readily convey the differences between the groups (Brockopp & Hastings-Tolsma, 2003).

Kruskal-Wallis test-more than two samples

The Kruskal-Wallis test is a simple non-parametric test to compare the medians of three or more samples. Observations may be interval measurements, counts of things, derived variables, or ordinal ranks. If there are only three samples, then there must be at least five observations in each sample. Samples do not have to be of equal sizes. The statistic K is used to indicate the test value.

Multivariate Analysis

Two-way 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 (one-way ANOVA is used with one independent variable and one dependent variable). The term factor is interchangeable with independent variable and factorial ANOVA therefore refers to the idea that data having two or more independent variables can be analyzed using this technique.

Analysis of Covariance (ANCOVA)

ANCOVA 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. Unlike other statistical techniques, these tests permit the investigator to examine several dependent and independent variables simultaneously.

Choosing the appropriate test

If the data fulfill the requirement of parametric assumptions, any of the parametric tests which suit the purpose can be used. O the other hand, if the data do not fulfill the parametric requirements, any of the non-parametric statistical tests, which suit the purpose, can be selected. Other factors which decide the selection of appropriate statistical tests are the number of independent and dependent variables, and he nature of the variables (whether nominal, ordinal, interval or ratio). When both independent and dependent variables are interval measures and are more than one, multiple correlation is the most appropriate statistic.  On the other hand when they are interval measures and their number is only one, Pearson r may be used. With ordinal and nominal measures, the non-parametric statistics are the common choice.

Computer Aided Analysis

The availability of computer software has greatly facilitated the execution of most statistical techniques. The many statistical packages run on different types of platforms or computer configurations. For general data analysis the Statistical Package for the Social Sciences (SPSS), the BMDP series, and the Statistical Analysis System (SAS) are recommended. These are general-purpose statistical packages that perform essentially all the analyses common to biomedical research. In addition, a variety of other packages have emerged.

SYSTAT runs on both IBM-compatible and Macintosh systems and performs most of the analyses commonly used in biomedical research. The popular SAS program has been redeveloped for Macintosh systems and is sold under the name JMP. Other commonly used programs include Stata, which is excellent for the IBM-compatible computers. The developers of Stata release a regular newsletter providing updates, which makes the package very attractive. StatView is a general-purpose program for the Macintosh computer.

Newer versions of StatView include an additional program called Super ANOVA, which is an excellent set of ANOVA routines. StatView is user-friendly and also has superb graphics. For users interested in epidemiological analyses, Epilog is a relatively low-cost program that runs on the IBM-compatible platforms. It is particularly valuable for rate calculations, analysis of disease-clustering patterns, and survival analysis. GB-STAT, is a low-cost, multipurpose package that is very comprehensive.

SPSS (Statistical Package for Social Sciences) is one among the popular computer programs for data analysis. This software provides a comprehensive set of flexible tools that can be used to accomplish a wide variety of data analysis tasks (Einspruch, 1998). SPSS is available in a variety of platforms. The latest product information and free tutorial are available at www.spss.com.

Computer software programs that provide easy access to highly sophisticated statistical methodologies represent both opportunities and dangers. On the positive side, no serious researcher need be concerned about being unable to utilize precisely the statistical technique that best suits his or her purpose, and to do so with the kind of speed and economy that was inconceivable just two decades ago. The danger is that some investigators may be tempted to employ after-the-fact statistical manipulations to salvage a study that was flawed to start with, or to extract significant findings through use of progressively more sophisticated multivariate techniques.

References & Bibliography

1. Ahuja R (2001). Research Methods. Rawat Publications, New Delhi. 71-72.
   
2. Brockopp D Y & Hastings-Tolsma M (2003). Fundamental of Nursing Research. 3rd Edition. Jones and Bartlet: Boston
   
3. Cozby P C (2000). Methods in Behavioral Research (7th Edition). Toronto: Mayfield Publishing Co.
   
4. Kerr A W, Hall H K, Kozub S A (2002). Doing Statistics with SPSS. Sage Publications, London.
   
5. Einspruch E L (1998). An Introductory Guide to SPSS for Windows. Sage Publications, Calf.
   
6. Fowler J, Jarvis P & Chevannes M (2002). Practical Statistics for Nursing and Health Care. John Wiley & Sons: England
   
7. Guilliford, J P (1956). Fundamental Statistics in Psychology and Education. New York: McGraw-Hill Book Co.
   
8. Lindquist, E F. (1968). Statistical Analysis in Educational Research.  New Delhi: Oxford and IBH Publishing Co.
   
9.  Singh AK. (2002). Tests, Measurements and Research Methods in Behavioural Sciences. Bharahty Bhavan. New Delhi.
   
10. Singlton, Royce A. and Straits, Bruce (1999). Approaches to Social Research (3rd Ed), Oxford University Press, New York.
    
11.  Streiner, D. & Norman, G. (1996). PDQ Epidemiology (2nd Edition). St. Louis: Mosbey
    
12.  Therese Baker L (1988). Doing Social Research, McGraw Hill Book Co., New York.
    
13. Treece E W & Treece J H (1989). Elements of Research in Nursing, The C.V. Mosby Co.,St.Louis.
    
14. Tyler L E (1963).Tests and Measurements. Englewood Cliffs, New Jersey: Prentice Hall, a-p7.b-p.14
    
15. Chalmers TC, Celano P, Sacks H, Smith H(1983). Bias in treatment assignment in controlled clinical trials. N Engl J Med 309:1358.
    
16. Cohen J (1988). Statistical Power Analysis for the Behavioral Sciences. Erlbaum, Hillsdale, NJ.
    
17. .Cook TD, Campbell DG(1979). Quasi-experimentation: Design and Analysis Issues for Field Studies. Rand-McNally, Chicago.
    
18. Daniel WW (1995) Biostatistics: A Foundation for Analysis in the Health Sciences, ed 6. Wiley, New York.
    
19. Daniel WW (1990). Applied Nonparametric Statistics, ed 2. PWS-Kent, Boston.
    
20. Dawson-Saunders B, Trapp RG (1994) Basic and Clinical Biostatistics, ed 2. Appleton & Lange, Norwalk, CT.
    
21. Edwards LK, editor (1993) Applied Analysis of Variance in Behavioral Science. Marcel Dekker, New York.
    
22. Efron B, Tibshirani R (1991). Statistical data analysis in the computer age. Science 253:390.
    
23. Jaccard J, Becker MA (1997). Statistics for the Behavioral Sciences, ed 3. Brooks/Cole Publishing Co, Pacific Grove, CA.
    
24. Keppel G (1991). Design and Analysis. Prentice-Hall, Englewood Cliffs, NJ.
    
25. Kaplan RM, Grant I, (200). Statistics and Experimental Design in Kaplan & Sadock's Comprehensive Textbook of Psychiatry 7th Edition.
    
26. McCall R (1994). Fundamental Statistics for Psychology, ed 6. Harcourt Brace, & Jovanovich, New York.
    
27. Pett MA (1997). Nonparametric Statistics for Health Care Research: Statistics for Small Samples and Unusual Distributions. Sage Publications, Thousand Oaks, CA.
    
28. Sacks H, Chalmers DC, Smith H (1982). Randomized versus historical controls for clinical trials. Am J Med 72:233.
    
29. Ware ME, Brewer CL, editors (1999). Handbook for Teaching Statistics and Research Methods, ed 2. Erlbaum, Mahwah, NJ.

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