Let's say I have data of a chemistry expriment: I have a sample of 11 probe coming from comparable material (ID01 to ID11, the random effect).
I make process them with 2 different reactants (reactant A and Reactant B, 2 different fixed effect).
There are 10 difference concentrations of reactant A and 3 different concentrations of reactant B.
I finally read a measurement and want to determine the effect of reactant A and reactant B.
The assumption is that the concentration of reactant A has an effect on the measurement, whereas reactant B does not.
I simulated data accordingly.
Part of the output is the following:
```
Fixed effects:
Estimate Std. Error t value
(Intercept) 367.786 27.395 13.425
Reac_A_num 4.319 2.917 1.481
Reac_B_num -0.693 10.369 -0.067
```
Here are my questions:
1. The absolute value of the estimate of Reac_A_num is greater than its Std. Error. Therefore, Reactant A seems to have an effect on the Outcome. Correct?
2. The absolute value of the estimate of Reac_B_num is smaller than its Std. Error. Therefore, Reactant B does not seem to have an effect on the Outcome. Correct?
3. If 1. and 2. are correct, how can one appropriately report those data in a scientific manuscript (as there are no "p-values")?
Here is the output
```
Linear mixed model fit by REML ['lmerMod']
Formula: Outcome ~ (1 | ID) + Reac_A_num + Reac_B_num
Data: dfcombined
REML criterion at convergence: 3936.1
Scaled residuals:
Min 1Q Median 3Q Max
-1.86549 -0.85212 0.01823 0.87264 1.81522
Random effects:
Groups Name Variance Std.Dev.
ID (Intercept) 0 0.0
Residual 22144 148.8
Number of obs: 308, groups: ID, 11
Fixed effects:
Estimate Std. Error t value
(Intercept) 367.786 27.395 13.425
Reac_A_num 4.319 2.917 1.481
Reac_B_num -0.693 10.369 -0.067
Correlation of Fixed Effects:
(Intr) Rc_A_n
Reac_A_num -0.579
Reac_B_num -0.746 -0.014
convergence code: 0
boundary (singular) fit: see ?isSingular
```
Here is the data set (in .csv format):
```
,ID,Reac_A,Reac_B,Outcome,Reac_A_num,Reac_B_num
0,ID01,Reac_A_C01,Reac_B_C01,175.96317549009538,1.0,1.0
1,ID02,Reac_A_C02,Reac_B_C01,182.2550618307917,2.0,1.0
2,ID03,Reac_A_C03,Reac_B_C01,143.91730930128176,3.0,1.0
3,ID04,Reac_A_C04,Reac_B_C01,131.6026369230803,4.0,1.0
4,ID05,Reac_A_C05,Reac_B_C01,148.19896459063142,5.0,1.0
5,ID06,Reac_A_C06,Reac_B_C01,130.09909959523614,6.0,1.0
6,ID07,Reac_A_C07,Reac_B_C01,146.56051256005466,7.0,1.0
7,ID08,Reac_A_C08,Reac_B_C01,141.57541963406646,8.0,1.0
8,ID09,Reac_A_C09,Reac_B_C01,149.58182187731092,9.0,1.0
9,ID10,Reac_A_C10,Reac_B_C01,193.91890183411255,10.0,1.0
10,ID11,Reac_A_C01,Reac_B_C01,190.33253022629935,1.0,1.0
11,ID01,Reac_A_C02,Reac_B_C01,207.37340937821955,2.0,1.0
12,ID02,Reac_A_C03,Reac_B_C01,,3.0,1.0
13,ID03,Reac_A_C04,Reac_B_C01,193.83089509653644,4.0,1.0
14,ID04,Reac_A_C05,Reac_B_C01,224.96359043837634,5.0,1.0
15,ID05,Reac_A_C06,Reac_B_C01,168.9277996502002,6.0,1.0
16,ID06,Reac_A_C07,Reac_B_C01,,7.0,1.0
17,ID07,Reac_A_C08,Reac_B_C01,177.11754211599552,8.0,1.0
18,ID08,Reac_A_C09,Reac_B_C01,228.46319787577542,9.0,1.0
19,ID09,Reac_A_C10,Reac_B_C01,194.59408911471948,10.0,1.0
20,ID10,Reac_A_C01,Reac_B_C01,224.93705465058832,1.0,1.0
21,ID11,Reac_A_C02,Reac_B_C01,239.81392794785458,2.0,1.0
22,ID01,Reac_A_C03,Reac_B_C01,268.36046471890825,3.0,1.0
23,ID02,Reac_A_C04,Reac_B_C01,306.6263050417395,4.0,1.0
24,ID03,Reac_A_C05,Reac_B_C01,215.78721903203765,5.0,1.0
25,ID04,Reac_A_C06,Reac_B_C01,264.5583036472632,6.0,1.0
26,ID05,Reac_A_C07,Reac_B_C01,,7.0,1.0
27,ID06,Reac_A_C08,Reac_B_C01,210.14827334408938,8.0,1.0
28,ID07,Reac_A_C09,Reac_B_C01,256.13323688501544,9.0,1.0
29,ID08,Reac_A_C10,Reac_B_C01,283.9991271496295,10.0,1.0
30,ID09,Reac_A_C01,Reac_B_C01,277.08503014205894,1.0,1.0
31,ID10,Reac_A_C02,Reac_B_C01,267.903873003556,2.0,1.0
32,ID11,Reac_A_C03,Reac_B_C01,281.3834178629039,3.0,1.0
33,ID01,Reac_A_C04,Reac_B_C01,,4.0,1.0
34,ID02,Reac_A_C05,Reac_B_C01,344.4271256530111,5.0,1.0
35,ID03,Reac_A_C06,Reac_B_C01,295.4412126363893,6.0,1.0
36,ID04,Reac_A_C07,Reac_B_C01,294.913964681868,7.0,1.0
37,ID05,Reac_A_C08,Reac_B_C01,279.0643560110288,8.0,1.0
38,ID06,Reac_A_C09,Reac_B_C01,265.73528808279366,9.0,1.0
39,ID07,Reac_A_C10,Reac_B_C01,269.594369031282,10.0,1.0
40,ID08,Reac_A_C01,Reac_B_C01,318.4978493512993,1.0,1.0
41,ID09,Reac_A_C02,Reac_B_C01,300.25815322306994,2.0,1.0
42,ID10,Reac_A_C03,Reac_B_C01,317.15900636894696,3.0,1.0
43,ID11,Reac_A_C04,Reac_B_C01,316.49810940434634,4.0,1.0
44,ID01,Reac_A_C05,Reac_B_C01,344.3703277261114,5.0,1.0
45,ID02,Reac_A_C06,Reac_B_C01,400.73832961881646,6.0,1.0
46,ID03,Reac_A_C07,Reac_B_C01,307.347866227025,7.0,1.0
47,ID04,Reac_A_C08,Reac_B_C01,359.6985341083482,8.0,1.0
48,ID05,Reac_A_C09,Reac_B_C01,349.6635070827579,9.0,1.0
49,ID06,Reac_A_C10,Reac_B_C01,314.3505809182711,10.0,1.0
50,ID07,Reac_A_C01,Reac_B_C01,339.3288205287455,1.0,1.0
51,ID08,Reac_A_C02,Reac_B_C01,369.276080590692,2.0,1.0
52,ID09,Reac_A_C03,Reac_B_C01,360.3857108994122,3.0,1.0
53,ID10,Reac_A_C04,Reac_B_C01,356.37934634764,4.0,1.0
54,ID11,Reac_A_C05,Reac_B_C01,368.71427173610505,5.0,1.0
55,ID01,Reac_A_C06,Reac_B_C01,424.8919327312468,6.0,1.0
56,ID02,Reac_A_C07,Reac_B_C01,447.77690494713124,7.0,1.0
57,ID03,Reac_A_C08,Reac_B_C01,397.24117528127516,8.0,1.0
58,ID04,Reac_A_C09,Reac_B_C01,409.5610092882836,9.0,1.0
59,ID05,Reac_A_C10,Reac_B_C01,409.84568484610554,10.0,1.0
60,ID06,Reac_A_C01,Reac_B_C01,366.10759468419167,1.0,1.0
61,ID07,Reac_A_C02,Reac_B_C01,375.58983850030506,2.0,1.0
62,ID08,Reac_A_C03,Reac_B_C01,424.925637139781,3.0,1.0
63,ID09,Reac_A_C04,Reac_B_C01,409.5605892723437,4.0,1.0
64,ID10,Reac_A_C05,Reac_B_C01,412.1493832561823,5.0,1.0
65,ID11,Reac_A_C06,Reac_B_C01,438.29488046013114,6.0,1.0
66,ID01,Reac_A_C07,Reac_B_C01,459.0904934575327,7.0,1.0
67,ID02,Reac_A_C08,Reac_B_C01,509.5730545010236,8.0,1.0
68,ID03,Reac_A_C09,Reac_B_C01,436.31133674925707,9.0,1.0
69,ID04,Reac_A_C10,Reac_B_C01,474.3985618234745,10.0,1.0
70,ID05,Reac_A_C01,Reac_B_C01,445.85919943449176,1.0,1.0
71,ID06,Reac_A_C02,Reac_B_C01,446.78098117824663,2.0,1.0
72,ID07,Reac_A_C03,Reac_B_C01,436.07093823665923,3.0,1.0
73,ID08,Reac_A_C04,Reac_B_C01,448.05246729255606,4.0,1.0
74,ID09,Reac_A_C05,Reac_B_C01,484.47105833287037,5.0,1.0
75,ID10,Reac_A_C06,Reac_B_C01,475.28623289390043,6.0,1.0
76,ID11,Reac_A_C07,Reac_B_C01,490.1614537977487,7.0,1.0
77,ID01,Reac_A_C08,Reac_B_C01,524.8742753611798,8.0,1.0
78,ID02,Reac_A_C09,Reac_B_C01,553.117235354672,9.0,1.0
79,ID03,Reac_A_C10,Reac_B_C01,455.74873612940326,10.0,1.0
80,ID04,Reac_A_C01,Reac_B_C01,527.7077201985376,1.0,1.0
81,ID05,Reac_A_C02,Reac_B_C01,487.17119575570837,2.0,1.0
82,ID06,Reac_A_C03,Reac_B_C01,488.1533401962364,3.0,1.0
83,ID07,Reac_A_C04,Reac_B_C01,489.0328612758312,4.0,1.0
84,ID08,Reac_A_C05,Reac_B_C01,496.40742171645616,5.0,1.0
85,ID09,Reac_A_C06,Reac_B_C01,,6.0,1.0
86,ID10,Reac_A_C07,Reac_B_C01,532.56564773395,7.0,1.0
87,ID11,Reac_A_C08,Reac_B_C01,492.0629677918874,8.0,1.0
88,ID01,Reac_A_C09,Reac_B_C01,572.5594461512935,9.0,1.0
89,ID02,Reac_A_C10,Reac_B_C01,588.3646944328207,10.0,1.0
90,ID03,Reac_A_C01,Reac_B_C01,526.364342594615,1.0,1.0
91,ID04,Reac_A_C02,Reac_B_C01,574.5303622287228,2.0,1.0
92,ID05,Reac_A_C03,Reac_B_C01,532.5390770818364,3.0,1.0
93,ID06,Reac_A_C04,Reac_B_C01,,4.0,1.0
94,ID07,Reac_A_C05,Reac_B_C01,549.7940269273572,5.0,1.0
95,ID08,Reac_A_C06,Reac_B_C01,535.3471348466327,6.0,1.0
96,ID09,Reac_A_C07,Reac_B_C01,586.148609110255,7.0,1.0
97,ID10,Reac_A_C08,Reac_B_C01,588.4265192761819,8.0,1.0
98,ID11,Reac_A_C09,Reac_B_C01,591.7855939629035,9.0,1.0
99,ID01,Reac_A_C10,Reac_B_C01,600.3192258875238,10.0,1.0
100,ID02,Reac_A_C01,Reac_B_C01,628.8892368256597,1.0,1.0
101,ID03,Reac_A_C02,Reac_B_C01,596.6412106335927,2.0,1.0
102,ID04,Reac_A_C03,Reac_B_C01,615.074165337679,3.0,1.0
103,ID05,Reac_A_C04,Reac_B_C01,567.9755977178145,4.0,1.0
104,ID06,Reac_A_C05,Reac_B_C01,597.0070121070032,5.0,1.0
105,ID07,Reac_A_C06,Reac_B_C01,606.3198305608295,6.0,1.0
106,ID08,Reac_A_C07,Reac_B_C01,630.707299481629,7.0,1.0
107,ID09,Reac_A_C08,Reac_B_C01,625.2529853544906,8.0,1.0
108,ID10,Reac_A_C09,Reac_B_C01,610.0952214989439,9.0,1.0
109,ID11,Reac_A_C10,Reac_B_C01,592.9134581323192,10.0,1.0
110,ID01,Reac_A_C01,Reac_B_C02,163.0947810916,1.0,2.0
111,ID02,Reac_A_C02,Reac_B_C02,175.40717115239784,2.0,2.0
112,ID03,Reac_A_C03,Reac_B_C02,181.6757774227178,3.0,2.0
113,ID04,Reac_A_C04,Reac_B_C02,157.49923701575278,4.0,2.0
114,ID05,Reac_A_C05,Reac_B_C02,160.87897823788632,5.0,2.0
115,ID06,Reac_A_C06,Reac_B_C02,149.9227018367978,6.0,2.0
116,ID07,Reac_A_C07,Reac_B_C02,119.0322974678176,7.0,2.0
117,ID08,Reac_A_C08,Reac_B_C02,201.32589035962877,8.0,2.0
118,ID09,Reac_A_C09,Reac_B_C02,199.72191356510584,9.0,2.0
119,ID10,Reac_A_C10,Reac_B_C02,225.13143123417257,10.0,2.0
120,ID11,Reac_A_C01,Reac_B_C02,180.189589558541,1.0,2.0
121,ID01,Reac_A_C02,Reac_B_C02,213.79571356719362,2.0,2.0
122,ID02,Reac_A_C03,Reac_B_C02,229.73876035471687,3.0,2.0
123,ID03,Reac_A_C04,Reac_B_C02,240.1213090822149,4.0,2.0
124,ID04,Reac_A_C05,Reac_B_C02,202.99916965232646,5.0,2.0
125,ID05,Reac_A_C06,Reac_B_C02,241.9260725758565,6.0,2.0
126,ID06,Reac_A_C07,Reac_B_C02,230.84150488548977,7.0,2.0
127,ID07,Reac_A_C08,Reac_B_C02,203.30128753977385,8.0,2.0
128,ID08,Reac_A_C09,Reac_B_C02,276.27506038513997,9.0,2.0
129,ID09,Reac_A_C10,Reac_B_C02,243.6251624306043,10.0,2.0
130,ID10,Reac_A_C01,Reac_B_C02,268.88966450756345,1.0,2.0
131,ID11,Reac_A_C02,Reac_B_C02,249.76155124412082,2.0,2.0
132,ID01,Reac_A_C03,Reac_B_C02,284.05893262218075,3.0,2.0
133,ID02,Reac_A_C04,Reac_B_C02,269.282305134721,4.0,2.0
134,ID03,Reac_A_C05,Reac_B_C02,280.6541003562467,5.0,2.0
135,ID04,Reac_A_C06,Reac_B_C02,250.08290055864364,6.0,2.0
136,ID05,Reac_A_C07,Reac_B_C02,268.2776774554918,7.0,2.0
137,ID06,Reac_A_C08,Reac_B_C02,246.97295832081502,8.0,2.0
138,ID07,Reac_A_C09,Reac_B_C02,261.15603294667596,9.0,2.0
139,ID08,Reac_A_C10,Reac_B_C02,316.8266580827621,10.0,2.0
140,ID09,Reac_A_C01,Reac_B_C02,,1.0,2.0
141,ID10,Reac_A_C02,Reac_B_C02,316.40792668666796,2.0,2.0
142,ID11,Reac_A_C03,Reac_B_C02,272.2695794164,3.0,2.0
143,ID01,Reac_A_C04,Reac_B_C02,315.00773094069035,4.0,2.0
144,ID02,Reac_A_C05,Reac_B_C02,297.4619449972508,5.0,2.0
145,ID03,Reac_A_C06,Reac_B_C02,,6.0,2.0
146,ID04,Reac_A_C07,Reac_B_C02,310.6044472652657,7.0,2.0
147,ID05,Reac_A_C08,Reac_B_C02,297.60363104852473,8.0,2.0
148,ID06,Reac_A_C09,Reac_B_C02,293.3535945837459,9.0,2.0
149,ID07,Reac_A_C10,Reac_B_C02,311.8844944544687,10.0,2.0
150,ID08,Reac_A_C01,Reac_B_C02,372.54824325955434,1.0,2.0
151,ID09,Reac_A_C02,Reac_B_C02,383.62324801824843,2.0,2.0
152,ID10,Reac_A_C03,Reac_B_C02,359.36045189004966,3.0,2.0
153,ID11,Reac_A_C04,Reac_B_C02,327.85876933184977,4.0,2.0
154,ID01,Reac_A_C05,Reac_B_C02,397.69539144291997,5.0,2.0
155,ID02,Reac_A_C06,Reac_B_C02,368.8278140497438,6.0,2.0
156,ID03,Reac_A_C07,Reac_B_C02,412.0278702683967,7.0,2.0
157,ID04,Reac_A_C08,Reac_B_C02,351.0515690015452,8.0,2.0
158,ID05,Reac_A_C09,Reac_B_C02,,9.0,2.0
159,ID06,Reac_A_C10,Reac_B_C02,357.53098627708755,10.0,2.0
160,ID07,Reac_A_C01,Reac_B_C02,351.76171766946663,1.0,2.0
161,ID08,Reac_A_C02,Reac_B_C02,431.5358020507246,2.0,2.0
162,ID09,Reac_A_C03,Reac_B_C02,411.5215514470504,3.0,2.0
163,ID10,Reac_A_C04,Reac_B_C02,424.455851691988,4.0,2.0
164,ID11,Reac_A_C05,Reac_B_C02,371.80841056316507,5.0,2.0
165,ID01,Reac_A_C06,Reac_B_C02,,6.0,2.0
166,ID02,Reac_A_C07,Reac_B_C02,439.008517979492,7.0,2.0
167,ID03,Reac_A_C08,Reac_B_C02,439.91287424424064,8.0,2.0
168,ID04,Reac_A_C09,Reac_B_C02,401.1288429486718,9.0,2.0
169,ID05,Reac_A_C10,Reac_B_C02,394.0433218413809,10.0,2.0
170,ID06,Reac_A_C01,Reac_B_C02,408.79052469358476,1.0,2.0
171,ID07,Reac_A_C02,Reac_B_C02,405.75078508310776,2.0,2.0
172,ID08,Reac_A_C03,Reac_B_C02,462.1378751411957,3.0,2.0
173,ID09,Reac_A_C04,Reac_B_C02,472.10133678400916,4.0,2.0
174,ID10,Reac_A_C05,Reac_B_C02,429.9382323866242,5.0,2.0
175,ID11,Reac_A_C06,Reac_B_C02,429.36175597917565,6.0,2.0
176,ID01,Reac_A_C07,Reac_B_C02,465.2208074595036,7.0,2.0
177,ID02,Reac_A_C08,Reac_B_C02,,8.0,2.0
178,ID03,Reac_A_C09,Reac_B_C02,475.8229302301139,9.0,2.0
179,ID04,Reac_A_C10,Reac_B_C02,465.7585274653326,10.0,2.0
180,ID05,Reac_A_C01,Reac_B_C02,490.9041036293007,1.0,2.0
181,ID06,Reac_A_C02,Reac_B_C02,452.899705296328,2.0,2.0
182,ID07,Reac_A_C03,Reac_B_C02,438.938018835665,3.0,2.0
183,ID08,Reac_A_C04,Reac_B_C02,498.98859501673553,4.0,2.0
184,ID09,Reac_A_C05,Reac_B_C02,516.7947826333289,5.0,2.0
185,ID10,Reac_A_C06,Reac_B_C02,522.4803392815998,6.0,2.0
186,ID11,Reac_A_C07,Reac_B_C02,488.35176146429575,7.0,2.0
187,ID01,Reac_A_C08,Reac_B_C02,525.3686475440222,8.0,2.0
188,ID02,Reac_A_C09,Reac_B_C02,510.4202171076454,9.0,2.0
189,ID03,Reac_A_C10,Reac_B_C02,570.0013095040155,10.0,2.0
190,ID04,Reac_A_C01,Reac_B_C02,504.85572031036577,1.0,2.0
191,ID05,Reac_A_C02,Reac_B_C02,494.03244524385883,2.0,2.0
192,ID06,Reac_A_C03,Reac_B_C02,534.4767844601406,3.0,2.0
193,ID07,Reac_A_C04,Reac_B_C02,486.8322427529967,4.0,2.0
194,ID08,Reac_A_C05,Reac_B_C02,561.0334582208496,5.0,2.0
195,ID09,Reac_A_C06,Reac_B_C02,570.494368858899,6.0,2.0
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328,ID10,Reac_A_C09,Reac_B_C03,623.4467116409456,9.0,3.0
329,ID11,Reac_A_C10,Reac_B_C03,561.0237102000497,10.0,3.0
```