Data Analysis and Interpretation

Concept

Processing prepares raw data for analysis, and Kothari lists the order as editing, coding, classification and tabulation. Editing checks completed instruments for errors, omissions and inconsistencies, either in the field or centrally. Coding assigns numerical or symbolic labels to responses, guided by a codebook. Classification groups data by attributes or by class intervals. Tabulation arranges the classified data in rows and columns; the parts of a table are the title, caption (column headings), stub (row labels), body, footnotes and source note. Data cleaning also deals with missing values and outliers.

Concept

The mean uses all values but is pulled by extremes; the median is the middle value and is best for skewed data or open-ended classes; the mode is the most frequent value and is the only average for nominal data. The geometric mean suits growth rates and the harmonic mean suits rates such as speed. In a symmetrical distribution all three coincide; in positive skew (long right tail) mean > median > mode; in negative skew mean \< median \< mode. Karl Pearson’s coefficient of skewness is (mean − mode) / SD. Kurtosis describes peakedness: leptokurtic (peaked), mesokurtic (normal), platykurtic (flat). The coefficient of variation (SD / mean × 100) compares variability between series with different units.

Concept

Inferential statistics draw conclusions about a population from a sample, through estimation (point and interval estimates, with confidence intervals) and hypothesis testing. Parametric tests (t, z, F) assume interval or ratio data and approximately normal distributions; non-parametric or distribution-free tests (chi-square, Mann–Whitney U, Wilcoxon, Kruskal–Wallis, sign test, Kolmogorov–Smirnov, Spearman) suit nominal or ordinal data, small samples and non-normal data. Degrees of freedom: for a chi-square test of independence df = (rows − 1)(columns − 1), so a 3 × 4 table has 6; for goodness of fit df = k − 1; for an independent-samples t-test df = n1 + n2 − 2.

Concept

Pearson’s product-moment r measures the strength and direction of a linear relationship between interval or ratio variables; Spearman’s rank correlation and Kendall’s tau serve ordinal data; point-biserial and phi coefficients handle a dichotomy. Partial and multiple correlation add control for or combine variables. Regression predicts one variable from another by the least-squares line y = a + bx, where b is the slope. The two regression lines intersect at the means, r² equals the product of the two regression coefficients (so r is their geometric mean, with the common sign), and r² is the coefficient of determination. Correlation, however high, does not prove cause, and spurious correlations arise from a third variable.

Concept

Interpretation draws meaning from analysed results by linking them to the hypotheses, earlier findings and theory, and by stating what they imply. It is the bridge between analysis and the report. Kothari’s precautions are to avoid generalising beyond the population studied, to check that the sample and tools were sound, not to infer cause from correlation alone, to keep extraneous factors and limitations in view, and to avoid selective reporting. Statistical significance is not the same as practical importance, so effect sizes (for example Cohen’s d) and confidence intervals should accompany p-values.