Data Analysis: Descriptive Statistics
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This document discusses quantitative data analysis and statistical measures. It describes levels of quantitative description, types of data analysis including descriptive and inferential analysis, and statistical measures used in descriptive analysis such as measures of central tendency, spread, relative position, and relationship. Specific statistical measures are defined, like mean, median, mode, range, variance, standard deviation, percentile scores, correlation coefficients, and when they are appropriate to use. Computational data analysis tools like IBM SPSS Statistics are also mentioned.
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Data Analysis: Descriptive Statistics
- 2. Synopsis Levels of Quantitative Description Types of Data Analysis Statistical Measures Applied to Descriptive Analysis Measures of central tendency/average Mean Median Mode Measure of spread/dispersion Range Variance Standard deviation Measure of relative position Standard scores Percentile rank Percentile score Measures of relationship Coefficient of correlation Computational Data Analysis
- 3. Scales of Quantitative Description Level Scale Process 4 Ratio Equal intervals True zero Ratio relationship 3 Interval Equal Intervals No true zero 2 Ordinal Data Ranked in order Descriptive Parametric Nonparametric 1 Nominal Classified and counted Some Appropriate Statistics Inferential Mean Standard deviation Pearson’s r Median Mann-Whitney Quartile deviation Wilcoxin Stanines Spearman’s rho (ρ) Mode Chi square Sign
- 4. Choosing Statistical Tests for Data
- 6. Descriptive and Inferential Analysis Descriptive Analysis Inferential Analysis Descriptive statistical analysis limits generalization to the particular group of individuals observed. That is: No conclusions are extended beyond this group. Any similarity to those outside the group cannot be assumed. The data describe one group and that group only. Examples: assessment findings, findings of a much simpler action research Inferential analysis selects a small group (sample) out of a larger group (population) and the finding are applied to the larger group. It is used to estimate a parameter, the corresponding value in the population from which the sample is selected. It is necessary to carefully select the sample or the inferences may not apply to the population.
- 7. Descriptive Analysis Statistical measures applied to descriptive data are as follows: Measures of central tendency/average Mean Median Mode Measure of spread/dispersion Range Variance Standard deviation Measure of relative position Standard scores Percentile rank Percentile score Measures of relationship Coefficient of correlation
- 10. Descriptive Analysis: Measure of Spread/Dispersion
- 11. Descriptive Analysis: Measure of Relative Position/Standard Scores
- 13. Measures of Relationship These indicate the degree of relationship (correlation coefficient) between two or more quantifiable variables from a single group of participants. The correlation can be positive (+), negative (-), or none . When one variable increases with the other, the correlation is positive; when one variable increases while the other decreases or the vice versa, the correlation is negative. There may be variables that have no correlation. A perfect positive correlation is +1; a perfect negative correlation is -1; a complete lack of correlation is 0. The sign of the coefficient indicates the direction of the relationship. A perfect positive correlation specifies that for every unit increase in one variable there is a proportional unit increase in the other. The perfect negative correlation specifies that for every unit increase in one variable there is a proportional unit decrease in the other.
- 14. Measures of Relationship: Pearson’s Product-Moment Coefficient of Correlation (r)
- 15. Measures of Relationship: Rank Order Correlation/Spearman’s rho (ρ)
- 16. Computational Data Analysis Computers are used to easily and flawlessly arrange and analyze data and apply statistical formulae. The following software programs can be used for this purpose: IBM SPSS Statistics Minitab MS Excel iNZight R
- 17. IBM SPSS Statistics integrates with a broad range of capabilities for the entire analytical process.
- 18. References and Further Reading Best, J. W., & Kahn, J. V. (2006). Research in Education (10th ed.). Pearson Education Inc. Cohen, L., Manion, L., & Morrison, K. (2011). Research Methods in Education (7th ed.). Routledge. Gay, L. R., & Geoffrey E. Mills, P. A. (2011). Educational Research: Competencies for Analysis and Applications (10th ed.). Pearson.
Editor's Notes
- #9: Mean counts all scores. It may be affected by extreme scores (both extremely high and extremely low). The average salary of a staff of 6 persons does not necessarily mean that the average is the least salary of a member of a staff.Median is the best index of typical score.The mode, in most cases, is less frequent than the values higher or lower than it.