Minimum sample size for estimating the Net Promoter Score under a Bayesian approach

COSTA, ELIARDO G.; PONTE, RACHEL TARINI Q.

doi:10.1590/0001-3765202420230091

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MATHEMATICAL SCIENCES • An. Acad. Bras. Ciênc. 96 (2) • 2024 • https://doi.org/10.1590/0001-3765202420230091 copy

Minimum sample size for estimating the Net Promoter Score under a Bayesian approach

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

At some moment in our lives, we are probably faced with the following question: How likely is it that you would recommend [company X] to a friend or colleague?. This question is related to the Net Promoter Score (NPS), a simple measure used by several companies as indicator of customer loyalty. Even though it is a well-known measure in the business world, studies that address the statistical properties or the sample size determination problem related to this measure are still scarce. We adopt a Bayesian approach to provide point and interval estimators for the NPS and discuss the determination of the sample size. Computational tools were implemented to use this methodology in practice. An illustrative example with data from financial services is also presented.

Key words
Average length criterion; customer loyalty; Dirichlet distribution multinomial distribution; sample size

ℓ_max \𝜌	(0.1, 0.1, 0.1)			(0.99, 0.99, 0.99)
ℓ_max \𝜌	0.01	0.05	0.10	0.01	0.05	0.10
0.02	4406	2482	1753	28406	16048	11222
0.04	1089	629	415	7073	4033	2836
0.06	531	295	200	3148	1801	1270
0.08	311	167	109	1822	995	690
0.10	202	108	70	1148	639	457
0.12	147	78	48	808	458	319
0.14	110	57	36	593	333	235
0.16	90	43	27	447	258	178
0.18	71	32	23	355	201	141
0.20	57	27	18	290	161	115
ℓ_max \ 𝜌	(1, 1, 1)			(5, 5, 5)
ℓ_max \ 𝜌	0.01	0.05	0.10	0.01	0.05	0.10
0.02	28199	16034	11328	37737	21516	15157
0.04	7153	4085	2805	9521	5396	3810
0.06	3222	1808	1272	4243	2386	1681
0.08	1786	992	721	2391	1330	944
0.10	1158	655	460	1515	860	599
0.12	807	460	315	1046	590	409
0.14	591	334	234	764	433	298
0.16	452	249	179	585	326	224
0.18	359	203	142	464	254	175
0.20	291	164	114	371	204	139
ℓ_max \ 𝜌	(50, 50, 50)			(100, 100, 100)
ℓ_max \ 𝜌	0.01	0.05	0.10	0.01	0.05	0.10
0.02	40494	22924	16116	40670	22987	16007
0.04	10085	5666	3951	10004	5532	3796
0.06	4411	2435	1668	4286	2285	1520
0.08	2422	1313	876	2283	1157	728
0.10	1505	781	501	1355	637	358
0.12	991	500	310	848	348	159
0.14	685	326	187	550	178	37
0.16	490	216	107	346	67	2
0.18	357	138	53	208	2	2
0.20	266	82	15	116	2	2

ℓ_max\𝜌	(2, 5, 8)			(4, 10, 16)
ℓ_max\𝜌	0.01	0.05	0.10	0.01	0.05	0.10
0.02	28494	16105	11346	29723	16796	11841
0.04	7116	4018	2816	7509	4207	2949
0.06	3198	1790	1258	3303	1857	1304
0.08	1779	1004	698	1847	1033	720
0.10	1137	636	442	1169	645	449
0.12	788	442	307	809	449	305
0.14	577	322	225	586	322	217
0.16	433	243	166	444	236	156
0.18	342	189	130	340	182	119
0.20	275	150	100	275	139	91
ℓ_max\𝜌	(8, 20, 32)			(16, 40, 64)
ℓ_max\𝜌	0.01	0.05	0.10	0.01	0.05	0.10
0.02	30537	17235	12072	30811	17349	12124
0.04	7614	4256	2988	7640	4291	2985
0.06	3368	1874	1302	3343	1842	1261
0.08	1840	1034	708	1833	982	654
0.10	1180	643	431	1127	587	373
0.12	801	425	284	742	373	223
0.14	574	297	190	517	242	136
0.16	426	215	133	372	157	76
0.18	323	156	93	264	101	35
0.20	248	116	63	194	56	7

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[1] Correspondence to: Eliardo G. Costa E-mail: eliardo.costa@ufrn.br