fishersMetaAnalysis.xlsx

	A	B	C	D	E	F	G	H	I	J	K	L	M
1	Simple spreadsheet implementing Fisher's method for meta-analysis, Strouffer's method, and an empircal rule of thumb that is shown to be close to Stouffer
2	By Ronny Kohavi
3	https://bit.ly/metaAnalysisRonnyK
4
5
6	4/9/2023 Note: Fisher's method in the original spreadsheet had a bug, where the density function was used instead of the right tail. Thanks to Yevhen Kralych for pointing this out
7	Strangely, the corrected Fisher's method does not align with Stouffer, as it did before. Alex Deng and Georgi Georgiev have both look at this and confirmed the new numbers look correct.
8	1/26/2024: If we're looking at two treatment effects that are aligned, then we should halve the p-value for one-tail. Added column for Fisher's aligned direction.
9	This makes the two methods much closer
10
11
12	P-value 1	0.1
13	P-value 2	0.1
14	Fisher's p-value	0.05605170186	Wikipedia says two 0.1 combined is 0.05
15	Fisher's aligned	0.01747866137
16	Stouffer	0.02000925385
17
19	Val1	Val2	Fisher's method Chi^2	Fisher's two-tailed p-value	Fisher's method with direction alignment	Fisher's aligned direction p-value	Z-score1	Z-score2	Stouffer	P-value Stouffer	Delta	Ronny's Rule of thumb (2p1p2)	Delta
20	0.15	0.15	7.58847994	0.1078703993	10.36106866	0.03476550561	-1.439531472	-1.439531472	-2.035804932	0.041770	-0.066100	0.045	0.003230
21	0.14	0.14	7.864451425	0.09667162397	10.63704015	0.03096074836	-1.47579103	-1.47579103	-2.08708369	0.036881	-0.059791	0.0392	0.002319
22	0.13	0.13	8.160883314	0.085859464	10.93347204	0.02732195968	-1.514101889	-1.514101889	-2.141263426	0.032253	-0.053607	0.0338	0.001547
23	0.12	0.12	8.481054145	0.07546358984	11.25364287	0.02385655716	-1.554773595	-1.554773595	-2.198781904	0.027893	-0.047570	0.0288	0.000907
24	0.11	0.11	8.829099653	0.0655160529	11.60168837	0.02057255367	-1.598193139	-1.598193139	-2.260186412	0.023810	-0.041706	0.0242	0.000390
25	0.1	0.1	9.210340372	0.05605170186	11.98292909	0.01747866137	-1.644853625	-1.644853625	-2.326174305	0.020009	-0.036042	0.02	-0.000009
26	0.09	0.09	9.631782435	0.04710871886	12.40437116	0.0145844258	-1.69539771	-1.69539771	-2.397654435	0.016500	-0.030608	0.0162	-0.000300
27	0.08	0.08	10.10291458	0.03872932665	12.8755033	0.01190040264	-1.750686073	-1.750686073	-2.475843988	0.013292	-0.025437	0.0128	-0.000492
28	0.07	0.07	10.63704015	0.03096074836	13.40962887	0.009438397683	-1.811910674	-1.811910674	-2.562428649	0.010394	-0.020566	0.0098	-0.000594
29	0.06	0.06	11.25364287	0.02385655716	14.02623159	0.007211804215	-1.880793606	-1.880793606	-2.659843826	0.007818	-0.016039	0.0072	-0.000618
30	0.05	0.05	11.98292909	0.01747866137	14.75551782	0.005236099318	-1.959963986	-1.959963986	-2.771807651	0.005575	-0.011904	0.005	-0.000575
31	0.04	0.04	12.8755033	0.01190040264	15.64809202	0.003529618404	-2.053748909	-2.053748909	-2.904439561	0.003679	-0.008221	0.0032	-0.000479
32	0.03	0.03	14.02623159	0.007211804215	16.79882031	0.002114867285	-2.170090375	-2.170090375	-3.068971241	0.002148	-0.005064	0.0018	-0.000348
33	0.02	0.02	15.64809202	0.003529618404	18.42068074	0.001021034037	-2.326347874	-2.326347874	-3.289952715	0.001002	-0.002528	0.0008	-0.000202
34	0.01	0.01	18.42068074	0.001021034037	21.19326947	0.0002899158683	-2.575829306	-2.575829306	-3.64277274	0.000270	-0.000751	0.0002	-0.000070
35	0.009	0.009	18.84212281	0.0008441059737	21.61471153	0.0002390989542	-2.612054144	-2.612054144	-3.694002396	0.000221	-0.000623	0.000162	-0.000059
36	0.008	0.008	19.31325495	0.0006820241584	22.08584367	0.0001926867494	-2.652069811	-2.652069811	-3.750593095	0.000176	-0.000506	0.000128	-0.000048
37	0.007	0.007	19.84738052	0.0005352608227	22.61996924	0.0001507973116	-2.696844264	-2.696844264	-3.813913733	0.000137	-0.000398	0.000098	-0.000039
38	0.006	0.006	20.46398324	0.0004043516983	23.23657196	0.0001135645738	-2.747781388	-2.747781388	-3.885949705	0.000102	-0.000302	0.000072	-0.000030
39	0.005	0.005	21.19326947	0.0002899158683	23.96585819	0.00008114330684	-2.80703377	-2.80703377	-3.969745228	0.000072	-0.000218	0.00005	-0.000022
40	0.004	0.004	22.08584367	0.0001926867494	24.85843239	0.00005371686479	-2.87816174	-2.87816174	-4.070335368	0.000047	-0.000146	0.000032	-0.000015
41	0.003	0.003	23.23657196	0.0001135645738	26.00916068	0.00003151030577	-2.967737925	-2.967737925	-4.197015224	0.000027	-0.000087	0.000018	-0.000009
42	0.002	0.002	24.85843239	0.00005371686479	27.63102112	0.00001481551056	-3.090232305	-3.090232305	-4.370248436	0.000012	-0.000041	0.000008	-0.000004
43	0.001	0.001	27.63102112	0.00001481551056	30.40360984	0.00000405045123	-3.290526728	-3.290526728	-4.653507526	0.000003	-0.000012	0.000002	-0.000001
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101