Statistical Analysis

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Statistics with Ms Excel
 Simple Statistics with Excel and Minitab
 Elementary Concepts in Statistics
 Multiple Regression
 ANOVA
Elementary Concepts in Statistics
Overview of Elementary Concepts in Statistics. In this introduction, we will briefly discuss those elementary statistical concepts that provide the necessary foundations for more specialized expertise in any area of statistical data analysis. The selected topics illustrate the basic assumptions of most statistical methods and/or have been demonstrated in research to be necessary components of one's general understanding of the "quantitative nature" of reality (Nisbett, et al., 1987). Because of space limitations, we will focus mostly on the functional aspects of the concepts discussed and the presentation will be very short. Further information on each of those concepts can be found in the Introductory Overview and Examples sections of this manual and in statistical textbooks. Recommended introductory textbooks are: Kachigan (1986), and Runyon and Haber (1976); for a more advanced discussion of elementary theory and assumptions of statistics, see the classic books by Hays (1988), and Kendall and Stuart (1979).

• What are variables?
• Correlational vs.
experimental research
• Dependent vs. independent
variables
• Measurement scales
• Relations between variables
• Why relations between
variables are important
• Two basic features of every
relation between variables
• What is "statistical
significance" (p-value)
• How to determine that a
result is "really" significant
• Statistical significance and
the number of analyses
performed
• Strength vs. reliability of a
• Why significance of a relation between
variables depends on the size of the sample
• Example: "Baby boys to baby girls ratio"
• Why small relations can be proven
significant only in large samples
• Can "no relation" be a significant result?
• How to measure the magnitude (strength) of
relations between variables
• Common "general format" of most statistical
tests
• How the "level of statistical significance" is
calculated
• Why the "Normal distribution" is important
• Illustration of how the normal distribution is
used in statistical reasoning (induction)
• Are all test statistics normally distributed?
• How do we know the consequences of
violating the normality assumption?
Statistics with Ms Excel 2
relation between variables
• Why stronger relations
between variables are more
significant
Use of Excel for Statistical Analysis
Neil Cox, Statistician, AgResearch Ruakura
Private Bag 3123, Hamilton, New Zealand
16 May 2000
This article gives an assessment of the practical implications of deficiencies reported by McCullough and Wilson (1999) in Excel’s statistical procedures. I outline what testing was done, discuss what deficiencies were found, assess the likely impact of the deficiencies, and give my opinion on the role of Excel in the analysis of data. My overall assessment is that, while Excel uses algorithms that are not robust and can lead to errors in extreme cases, the errors are very unlikely to arise in typical scientific data analysis in AgResearch.

THE DEFICIENCIES OF EXCEL’S STATISTICAL ALGORITHMS
What Aspects Were Examined?
Excel’s calculation of distributions (tail probabilities), mean and standard deviation calculations, analysis of variance, linear regression, non-linear regression (using Solver) and random numbers were scrutinised using data sets designed to reveal any shortcomings in the numerical procedures used in the calculations of statistics packages. The distributions were tested by Knusel (1998), the other aspects by McCullough and Wilson (1999). McCullough (1998, 1999) describes the methodology and the performance of SAS, SPSS and S-Plus.

How Did Excel Rate?
Generally Excel performed worse than the 3 statistics packages (SAS, SPSS, S-Plus) also examined, particularly in the non-linear regression problems. See below for...
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