Properties
Information about the chart is displayed in the Properties pane or (if you select an option from the Chart | Histogram) as summary information on the chart itself.
| Confidence Level | The confidence level is the amount of confidence that the true regression coefficients (a and b) will lie within the specified level. For example, by setting a 95% confidence level you can be 95% confident that the true regression coefficients lie somewhere within the confidence bands shown on the display. The bands represent the outer limits of all possible regression lines whose coefficients fall within that confidence level. |
| Mean | Mean (also known as the arithmetic mean or simple average) is a measure of the central tendency of the sample data. It is defined as the sum of the values (divided by the number of values (n). |
| Variance | The observed Variance of a random variable, probability distribution, or sample, is a measure of statistical dispersion, averaging the squared distance of its possible values from the expected value (mean). |
| Standard Deviation | This is the sample standard deviation of the values shown on the chart. The Standard Deviation is a measure of the spread of the data (the way in which they differ from the mean). |
| Regression Line (Reg Line) | A representation of the regression line, with the estimated coefficients a and b displayed beneath. |
| Correlation Coefficient (R) | The correlation coefficient, also known as the Pearson Correlation Coefficient, measures the strength of the linear relationship between the X and Y values. On the scattergram it represents the width of the point cloud. Perfectly correlated data would plot on a 45 degree line with R = 1. As the width of the cloud increases, the value of R decreases. R is always between -1 and +1. Values close to ±1 represent a strong relationship, whereas values close to 0 indicate a weak relationship. If R is positive, Y increases in proportion to X and the relationship is said to be positively correlated. If R is negative, Y decreases in proportion to X and the relationship is said to be negatively correlated. |
| R Squared | R Squared is the coefficient of determination and is the square of the correlation coefficient. The coefficient of determination is another indication of the quality of the regression and represents the reduction in total squared error compared with simply using the mean of Y as the predicted Y value. |
| Rank Correlation Coefficient (Rank Corr coef) | A limitation of the correlation coefficient is that it is affected by occasional extreme values. One way to minimise this effect is to sort both variables in increasing order and then analyse the sorted data. The same calculation is used to determine the correlation coefficient, but this time it is referred to as the Rank or Spearman Correlation Coefficient. The rank correlation coefficient does not require the relationship to be linear and may provide a better indication of correlation when extreme values are present. |
| xVar / yVar | The variance of the X value divided by the variance of the Y value. |
| Precision |
Precision is a measure of how well the Y value represents the X value. It is most commonly used in assay quality control (see "Geological Application" below), where X is the first assay value and Y is the matching repeat assay. |
Geological Application – Gold assay quality control (repeat assays)
Precision is an important parameter in assay quality control; in this application it is a measure of reproducibility of a result using the same method. For example gold assays might be analysed as Au1 for the first assay and Au2 for the repeat assay. The reproducibility of the repeat assays could be determined by plotting Au1 on the X-axis and Au2 on the Y-axis. If they were identical they would appear on a 45 degree line and would have a precision of zero. Deviations from this line can be explained using two parameters:
- Mean: Bias is present if the means are different. You can confirm the degree of difference by selecting Stats | Estimation of Mean | Difference Between Two Means from the main menu. Variations in sample recovery may influence the mean values.
- Precision: For gold, Fire Assay precision should ideally be less than 10% and Aqua Regia less than 15%, which are accepted industry standards. Precision values greater than these values indicate poor repeat analyses, which may be influenced by variations in geology and sampling technique.
Thus, if the mean of Au1 was 2g/t the precision for Fire Assay results incorporating both Au1 and Au2 could be expressed as 2 g/t ±10%.