34.5 Example: Removal efficiency

In wastewater treatment facilities, air from biofiltration is passed through a membrane and dissolved in water, and is transformed into harmless byproducts. The removal efficiency y (in %) may depend on the inlet temperature (in C; x).

The RQ is

In treating biofiltation wastewater, is the removal efficiency associated with the inlet temperature?

The population parameter is ρ, the correlation between the removal efficiency and inlet temperature.

A scatterplot of n=32 samples (Fig. 34.9) suggests an approximately linear relationship (Chitwood and Devinny 2001; Devore and Berk 2007). The output (jamovi: Fig. 34.10; SPSS: Fig. 34.11) shows that the sample correlation coefficient is r=0.891, and so R2=(0.891)2=79.4%. This means that about 79.4% of the variation in removal efficiency can be explained by knowing the inlet temperature.

The relationship between removal efficiency and inlet temperature

FIGURE 34.9: The relationship between removal efficiency and inlet temperature

To test if a relationship exists in the population, write:

  • H0: ρ=0;
  • H1: ρ0: Two-tailed (as implied by the RQ).

The software output (jamovi: Fig. 34.10; SPSS: Fig. 34.11) shows that P<0.001 (which is what P=0.000 in SPSS means). We conclude:

The sample presents very strong evidence (two-tailed P<0.001) that removal efficiency depends on the inlet temperature (r=0.891; n=32) in the population.

The relationship is approximately linear and there is no obvious non-constant variance, and the sample size is larger than 25, so the hypothesis test results will be statistically valid.

jamovi output for the removal-efficiency data

FIGURE 34.10: jamovi output for the removal-efficiency data

SPSS output for the removal-efficiency data

FIGURE 34.11: SPSS output for the removal-efficiency data

References

Chitwood DE, Devinny JS. Treatment of mixed hydrogen sulfide and organic vapors in a rock medium biofilter. Water Environment Research. Water Environment Federation; 2001;73(4):426–35.
Devore JL, Berk KN. Modern mathematical statistics with applications. Thomson Higher Education; 2007.