An introduction to statistical analysis

The meaning and importance of statistics; mathematics and non-mathematical aspects of statistics; variables and functions; sums and summations; remarks on measurement; decimal accuracy; significant figures; rounding off numbers; errors in calculations; the propagation of error.

Tabular and graphical representation: Frequency distribution: Classification of the data; the choice of the class interval; class limits; graphical representation; graphical representation of frequency distributions; graphical representation of temporal distributions; cumulative distributions and curves; types of frequency curves; suggestion for tabular and graphical presentation.

Measures of central tendency: The arithmetic mean, Mx; the arithmetic mean as a moment; a short method for computing the arithmetic mean; the median, Md; the mode, Mo; the geometric mean, Mg; the harmonic mean, Mh; discussion and criticism of the measures of central tendency.

Measurement of dispersion: The inadequacy of measures of central tendency; the range; the quartile deviation; the mean deviation; the standard deviation; the normal curve, the probable error; the significance of the mean and the standard deviation.

Skewness: Excess: Moments: The meaning of skewness; the measurement of skewness; excess or kurtosis; the unadjusted moments of a distribution; the adjusted moments: Sheppard's corrections; computation of the moments; retrospect and prospect.

Index numbers: Relative; definitions and notation; unweighted index numbers, weighting; weighted aggregates; weighted averages of relatives; summary and extension; bias; fisher's ideal index.

Linear trends: Some characteristic properties of a straight line; the equation of a straight line; fitting a straight line to observed data; the straight line with the origin at the centroidal point; fitting a straight line to a time series.

Simple correlation: Measures of concentration of points about the line of regression; the bravais-pearson coefficient of correlation; computation of r for ungrouped data; other forms of r; summary and extension of the theory of correlation; computation of r for grouped data; correlation by banks; correlation and causation.

Multiple correlation: The case of three variables; continuation of three variables; coefficient of multiple correlation for three variables; determinants of the second order, determinants of the third order, determinants of any order; application of determinants three variables; partial correlation; the case of four variables; the case of n variables.

Nonlinear trends: Curve-fitting: The process of differencing; fitting a straight line to observed data; the exponential function; the power function; the parabola; other useful curves; limitations of empirical equations; graphical methods in trend analysis, goodness of fit of curves to observed data: Nonlinear correlation.

Permutation, combination, and probability: Permutations; number of permutation; combinations; relative frequency: Empirical probability; theoretical relative frequency: A priori probability; expectation; some elementary theorems; repeated trials.

The point binomial and the normal curve: characteristics of the point binomial; the point binomial applied to frequency distribution; the normal curve: Introductory remarks; derivation of the equation to the normal curve; illustrative examples; on the significance of results; graduation of a distribution by normal curve.

The theory of sampling: Measures of reliability: The problem of this chapter; the standard deviation in class frequencies; an experiment in sampling; the distribution of mean; the reliability of the standard deviation; the reliability of the difference between two measures; small samples; concluding remarks on sampling; summary of reliability formulas.

Appendices: Areas and ordinates of the normal curve; four-place logarithms and antilogarithms answers to exercises.

Inglés