**4.3 Acid Pre-treatment**

**4.3.1 Statistical Analysis of Acid Pre-treatment Results**

**4.3.1.1 Assumptions and Considerations for the t-Test and ANOVA **

The experimental repeatability test was carried out by determining the closeness of the results of
each experimental run and the corresponding duplicate. This was achieved by using a *two-sample *
*t-test with matched samples*. The samples (run and duplicate) were matched because the data
points were collected at equal time intervals. The null hypothesis *H**0* for this t-test was that the two
samples, i.e. experimental results of the run and duplicate, were indicative of the same
experimental conditions (Montgomery, 2017). The null hypothesis for this test can also be
expressed as follows:

- The two samples (data sets) have the same probability distribution.

- The two samples belong to the same population.

The *two-factor ANOVA (analysis of variance) with replication* was carried out to investigate the
main factor effects and their interactions. The duplicates are specifically included to provide
insights into factor interactions (DeCoursey, 2003). Finally, the *estimated marginal means* were
used to add emphasis to the effect sizes of the factors investigated. The null hypothesis *H**0* of
ANOVA was that the factor variations would have no significant impact on the response variables.

The alternative or research hypothesis *H**a* was that varying the factors would have a statistically
significant effect on the response variables.

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The following assumptions and considerations were upheld for the t-test and ANOVA to provide simplicity and practicality to the statistical analysis:

- The t-tests and ANOVAs were based on response means for each run (Montgomery, 2017).

- All samples were drawn from normally distributed overall populations.

- No post hoc testing was carried out for the ANOVA because the factors investigated in acid pre-treatment and ammonium thiosulphate leaching had two levels only. In general, post hoc tests, aimed at determining the most significant factors, are carried out for factors with more than two levels (Weinberg & Abramowitz, 2008).

- Performing multiple ANOVAs is known to be detrimental to the data analysis because it
increases the experiment-wise error. However, for this research, two ANOVAs were
carried out to accommodate two responses, i.e. Cu and Au extractions in acid pre-
treatment, and Au extraction and thiosulphate consumption in ammonium thiosulphate
leaching. Therefore, to maintain the experiment-wise error or type I error (alpha) at 0.05,
the *Bonferroni correction* 𝛼 = 1 − (1 − 𝛼_{1})(1 − 𝛼_{2}) … (1 − 𝛼_{3}) was used, whereby the
alpha value was adjusted to 𝛼_{1}= 𝛼_{2}= 0.0253 for both Anovas (Norman & Streiner, 2008).

The above assumptions and considerations were adopted for both the acid pre-treatment results and ammonium thiosulphate leaching results.

**4.3.1.2 Experimental Repeatability Test **

Detailed t-test results are tabulated in Appendix C (Tables Table C-7 and Table C-8). The alpha values for all four conditions and both responses were less than 0.05, indicating that there were no statistical grounds for rejecting the null hypothesis that the run and duplicate results were indicative of the same experimental conditions. The following two observations further supported this result: (i) the t-statistic was less than the t-critical in the t-distribution and (ii) the Pearson correlation coefficients were close to 1 for all conditions. Therefore, the experimental repeatability was confirmed statistically.

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**4.3.1.3 Analysis of Variance (ANOVA) – Acid Pre-treatment **

The ANOVA results for the acid pre-treatment experiments are fully provided in Appendix C (Table C-11). The factor significance and interactions can be assessed with the aid of three statistical variables, namely the p-value, F-statistic and partial eta squared. Furthermore, since a dual analysis of variance was carried out for the Cu extraction (response 1) and Au extraction (response 2), the alpha value was adjusted to 0.0253 to maintain the threshold of the overall experiment-wise error at 0.05.

The effect of varying H2SO4 concentration was not statistically significant for copper extraction but was significant for gold extraction based on the p-value and F-statistic which were found to be 0.208 and 2.255, respectively for copper extraction, and 0.006 and 28.115, respectively for gold extraction. The variation in H2O2 concentration, on the other hand, was found to be significant for Cu extraction and not statistically significant for Au extraction. Hydrogen peroxide was the oxidant involved in the acid leaching of copper and was thus expected to influence the extent of copper extraction. Therefore, based on these results, one can infer that varying sulphuric acid concentration had more statistical impact on the gold extraction, and varying hydrogen peroxide concentration had more effect on the copper extraction.

The most critical observation on the ANOVA results was the significant interaction between the sulphuric acid and hydrogen peroxide concentrations which was substantiated by the extremely low p-values (0.004 for Cu extraction and 0.001 for Au extraction), high F-statistics (34.214 for Cu extraction and 73.062 for Au extraction), and visually by the crossing of the estimated marginal means lines of the interaction plots in Figure 4-5. Elliott & Woodward (2014) suggested that when a significant interaction between factors has been established statistically, it becomes difficult to isolate the individual effects of each factor because the factors are too intertwined to be examined individually. The factor interaction was supported by the results plotted in Figure 4-2 which indicated that the variability in copper and gold extraction were not apparent for the major part of the leaching process irrespective of the investigated conditions, with the difference showing towards the end of acid pre-treatment process (after 120 min of leaching time).

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(a) (b)

**Figure 4-5: Factor interaction plots for acid pre-treatment: (a) Cu extraction and (b) Au extraction **