Table 4.

Probability Calculations for Organic Detection in Icy Moon Samples with Varying True Positive Rates and True Negative Rates and Different Associated Positive Likelihood Ratios

	← Method with increasing TPR, TNR, and LHRs
Organic compounds
True positive rate = true positives/(true positives + false negatives)	0.99	0.95	0.90	0.75	0.60	0.50
True negative rate = true negatives/(true negatives + false positives)	0.99	0.95	0.90	0.75	0.60	0.50
Positive likelihood ratio = true positive rate/(1 − true negative rate)	99.0	19.00	9.00	3.00	1.50	1.00
Premeasurement probability (fraction of particles with the analyte)	0.25	0.25	0.25	0.25	0.25	0.25
Premeasurement odds = probability/(1 – probability)	0.33	0.33	0.33	0.33	0.33	0.33
Postmeasurement odds = premeasurement odds × likelihood ratio	33.0	6.33	3.00	1.00	0.50	0.33
Postmeasurement probability = odds/(1 + odds)	0.97	0.86	0.75	0.50	0.33	0.25
Postmeasurement probability (%)	97	86	75	50	33	25
Complex >200 amu organic matter
True positive rate = true positives/(true positives + false negatives)	0.99	0.95	0.90	0.75	0.60	0.50
True negative rate = true negatives/(true negatives + false positives)	0.99	0.95	0.90	0.75	0.60	0.50
Positive likelihood ratio = true positive rate/(1 − true negative rate)	99.0	19.0	9.00	3.00	1.50	1.00
Premeasurement probability (fraction of particles with the analyte)	0.03	0.03	0.03	0.03	0.03	0.03
Premeasurement odds = probability/(1 − probability)	0.03	0.03	0.03	0.03	0.03	0.03
Postmeasurement odds = premeasurement odds × likelihood ratio	3.06	0.59	0.28	0.09	0.05	0.03
Postmeasurement probability = odds/(1 + odds)	0.75	0.37	0.22	0.08	0.04	0.03
Postmeasurement probability (%)	75	37	22	8	4	3

Single measurements are likely in the icy moon environment; so very high positive likelihood ratios will provide the best certainty of detection.

LHR = likelihood ratio; TNR = true negative ratio; TPR = true positive ratio.