Advertising Statistics

I recently rediscovered an advert I have been trying to find for ages because it is a classic example of the spurious use of misleading figures in advertising and really irritated me when I saw it many months ago. It recently appeared very briefly in Charlie Brooker's advertising edition of Screenwipe.

The product is L'Oreal Collegen Replumper and one thing that struck me the first time I saw it is the very odd numbers used to justify the products claims, as seen in the screenshot below:



Firstly, 217 women is a ridiculously small control group for testing a naturally distributed cosmetic product.

Secondly, the figures don't add up:
"Plumps and Smooths, 81% agree" out of "217 women tested"
Let's do the math:
How much is 81% of 217?:
81/100=0.81
0.81 x 217= 175.77 women.

175.77 women agree?
175.77 women?!

OK, maybe this isn't fair: if a survey is taken, some women may choose not to answer the question, in which case, they would not be counted as one of the 81%, even though they could be counted as one of the 217. In this case we can work out the amount of women who agreed with the statement by multiplying 0.81 by every number between 217 and 1 and finding out which numbers give non-decimal integers:

No. of women tested	81% of No. of women tested		No. of women tested	81% of No. of women tested
217	175.77		97	78.57
216	174.96		96	77.76
215	174.15		95	76.95
214	173.34		94	76.14
213	172.53		93	75.33
212	171.72		92	74.52
211	170.91		91	73.71
210	170.1		90	72.9
209	169.29		89	72.09
208	168.48		88	71.28
207	167.67		87	70.47
206	166.86		86	69.66
205	166.05		85	68.85
204	165.24		84	68.04
203	164.43		83	67.23
202	163.62		82	66.42
201	162.81		81	65.61
200	162		80	64.8
199	161.19		79	63.99
198	160.38		78	63.18
197	159.57		77	62.37
196	158.76		76	61.56
195	157.95		75	60.75
194	157.14		74	59.94
193	156.33		73	59.13
192	155.52		72	58.32
191	154.71		71	57.51
190	153.9		70	56.7
189	153.09		69	55.89
188	152.28		68	55.08
187	151.47		67	54.27
186	150.66		66	53.46
185	149.85		65	52.65
184	149.04		64	51.84
183	148.23		63	51.03
182	147.42		62	50.22
181	146.61		61	49.41
180	145.8		60	48.6
179	144.99		59	47.79
178	144.18		58	46.98
177	143.37		57	46.17
176	142.56		56	45.36
175	141.75		55	44.55
174	140.94		54	43.74
173	140.13		53	42.93
172	139.32		52	42.12
171	138.51		51	41.31
170	137.7		50	40.5
169	136.89		49	39.69
168	136.08		48	38.88
167	135.27		47	38.07
166	134.46		46	37.26
165	133.65		45	36.45
164	132.84		44	35.64
163	132.03		43	34.83
162	131.22		42	34.02
161	130.41		41	33.21
160	129.6		40	32.4
159	128.79		39	31.59
158	127.98		38	30.78
157	127.17		37	29.97
156	126.36		36	29.16
155	125.55		35	28.35
154	124.74		34	27.54
153	123.93		33	26.73
152	123.12		32	25.92
151	122.31		31	25.11
150	121.5		30	24.3
149	120.69		29	23.49
148	119.88		28	22.68
147	119.07		27	21.87
146	118.26		26	21.06
145	117.45		25	20.25
144	116.64		24	19.44
143	115.83		23	18.63
142	115.02		22	17.82
141	114.21		21	17.01
140	113.4		20	16.2
139	112.59		19	15.39
138	111.78		18	14.58
137	110.97		17	13.77
136	110.16		16	12.96
135	109.35		15	12.15
134	108.54		14	11.34
133	107.73		13	10.53
132	106.92		12	9.72
131	106.11		11	8.91
130	105.3		10	8.1
129	104.49		9	7.29
128	103.68		8	6.48
127	102.87		7	5.67
126	102.06		6	4.86
125	101.25		5	4.05
124	100.44		4	3.24
123	99.63		3	2.43
122	98.82		2	1.62
121	98.01		1	0.81
120	97.2
119	96.39
118	95.58
117	94.77
116	93.96
115	93.15
114	92.34
113	91.53
112	90.72
111	89.91
110	89.1
109	88.29
108	87.48
107	86.67
106	85.86
105	85.05
104	84.24
103	83.43
102	82.62
101	81.81
100	81
99	80.19
98	79.38

As you can see by the chart above, the only possible number of women who could have agreed with the statement are either 200 women or 100 women; either 17 or 117 less than their advert implies: that's either 7.83% or 53.91% less - bringing the possibly of a major discrepancy between the figures presented and the actual 'research' carried out!

Needless to say, I should get out more.

dp