char = B;code = 66
char = e;code = 101
char = y;code = 121
char = o;code = 111
char = n;code = 110
char = d;code = 100
char = ;code = 32
char = p;code = 112
char = -;code = 45
char = v;code = 118
char = a;code = 97
char = l;code = 108
char = u;code = 117
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = e;code = 101
char = v;code = 118
char = a;code = 97
char = l;code = 108
char = u;code = 117
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = o;code = 111
char = n;code = 110
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = b;code = 98
char = r;code = 114
char = a;code = 97
char = i;code = 105
char = n;code = 110
char = -;code = 45
char = c;code = 99
char = o;code = 111
char = m;code = 109
char = p;code = 112
char = u;code = 117
char = t;code = 116
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = t;code = 116
char = e;code = 101
char = r;code = 114
char = f;code = 102
char = a;code = 97
char = c;code = 99
char = e;code = 101
char = s;code = 115
char = :;code = 58
char = ;code = 32
char = a;code = 97
char = ;code = 32
char = B;code = 66
char = a;code = 97
char = y;code = 121
char = e;code = 101
char = s;code = 115
char = i;code = 105
char = a;code = 97
char = n;code = 110
char = ;code = 32
char = e;code = 101
char = s;code = 115
char = t;code = 116
char = i;code = 105
char = m;code = 109
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = o;code = 111
char = n;code = 110
char = ;code = 32
char = a;code = 97
char = p;code = 112
char = p;code = 112
char = r;code = 114
char = o;code = 111
char = a;code = 97
char = c;code = 99
char = h;code = 104
char = .;code = 46
result sql = Beyond p-values in the evaluation of brain-computer interfaces: a Bayesian estimation approach.

Beyond p-values in the evaluation of brain-computer interfaces: a Bayesian estimation approach.

char = T;code = 84
char = o;code = 111
char = ;code = 32
char = s;code = 115
char = t;code = 116
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = s;code = 115
char = t;code = 116
char = i;code = 105
char = c;code = 99
char = a;code = 97
char = l;code = 108
char = l;code = 108
char = y;code = 121
char = ;code = 32
char = e;code = 101
char = v;code = 118
char = a;code = 97
char = l;code = 108
char = u;code = 117
char = a;code = 97
char = t;code = 116
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = e;code = 101
char = r;code = 114
char = f;code = 102
char = o;code = 111
char = r;code = 114
char = m;code = 109
char = a;code = 97
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = b;code = 98
char = r;code = 114
char = a;code = 97
char = i;code = 105
char = n;code = 110
char = -;code = 45
char = c;code = 99
char = o;code = 111
char = m;code = 109
char = p;code = 112
char = u;code = 117
char = t;code = 116
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = t;code = 116
char = e;code = 101
char = r;code = 114
char = f;code = 102
char = a;code = 97
char = c;code = 99
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = (;code = 40
char = B;code = 66
char = C;code = 67
char = I;code = 73
char = s;code = 115
char = );code = 41
char = ,;code = 44
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = s;code = 115
char = e;code = 101
char = a;code = 97
char = r;code = 114
char = c;code = 99
char = h;code = 104
char = e;code = 101
char = r;code = 114
char = s;code = 115
char = ;code = 32
char = u;code = 117
char = s;code = 115
char = u;code = 117
char = a;code = 97
char = l;code = 108
char = l;code = 108
char = y;code = 121
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = l;code = 108
char = y;code = 121
char = ;code = 32
char = o;code = 111
char = n;code = 110
char = ;code = 32
char = n;code = 110
char = u;code = 117
char = l;code = 108
char = l;code = 108
char = ;code = 32
char = h;code = 104
char = y;code = 121
char = p;code = 112
char = o;code = 111
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = s;code = 115
char = i;code = 105
char = s;code = 115
char = ;code = 32
char = s;code = 115
char = i;code = 105
char = g;code = 103
char = n;code = 110
char = i;code = 105
char = f;code = 102
char = i;code = 105
char = c;code = 99
char = a;code = 97
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = e;code = 101
char = s;code = 115
char = t;code = 116
char = i;code = 105
char = n;code = 110
char = g;code = 103
char = ;code = 32
char = (;code = 40
char = N;code = 78
char = H;code = 72
char = S;code = 83
char = T;code = 84
char = );code = 41
char = ,;code = 44
char = ;code = 32
char = i;code = 105
char = .;code = 46
char = e;code = 101
char = .;code = 46
char = ;code = 32
char = p;code = 112
char = -;code = 45
char = v;code = 118
char = a;code = 97
char = l;code = 108
char = u;code = 117
char = e;code = 101
char = s;code = 115
char = .;code = 46
char = ;code = 32
char = H;code = 72
char = o;code = 111
char = w;code = 119
char = e;code = 101
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = ,;code = 44
char = ;code = 32
char = o;code = 111
char = v;code = 118
char = e;code = 101
char = r;code = 114
char = -;code = 45
char = r;code = 114
char = e;code = 101
char = l;code = 108
char = i;code = 105
char = a;code = 97
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = n;code = 110
char = ;code = 32
char = N;code = 78
char = H;code = 72
char = S;code = 83
char = T;code = 84
char = ;code = 32
char = i;code = 105
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = t;code = 116
char = e;code = 101
char = n;code = 110
char = ;code = 32
char = i;code = 105
char = d;code = 100
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = i;code = 105
char = f;code = 102
char = i;code = 105
char = e;code = 101
char = d;code = 100
char = ;code = 32
char = a;code = 97
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = n;code = 110
char = e;code = 101
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = c;code = 99
char = a;code = 97
char = u;code = 117
char = s;code = 115
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = r;code = 114
char = e;code = 101
char = c;code = 99
char = e;code = 101
char = n;code = 110
char = t;code = 116
char = ;code = 32
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char = r;code = 114
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char = d;code = 100
char = u;code = 117
char = c;code = 99
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char = b;code = 98
char = i;code = 105
char = l;code = 108
char = i;code = 105
char = t;code = 116
char = y;code = 121
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char = c;code = 99
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char = i;code = 105
char = s;code = 115
char = i;code = 105
char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = p;code = 112
char = s;code = 115
char = y;code = 121
char = c;code = 99
char = h;code = 104
char = o;code = 111
char = l;code = 108
char = o;code = 111
char = g;code = 103
char = y;code = 121
char = ;code = 32
char = a;code = 97
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char = d;code = 100
char = ;code = 32
char = n;code = 110
char = e;code = 101
char = u;code = 117
char = r;code = 114
char = o;code = 111
char = s;code = 115
char = c;code = 99
char = i;code = 105
char = e;code = 101
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = .;code = 46
char = <;code = 60
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char = >;code = 62
char = I;code = 73
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char = ;code = 32
char = t;code = 116
char = h;code = 104
char = i;code = 105
char = s;code = 115
char = ;code = 32
char = p;code = 112
char = a;code = 97
char = p;code = 112
char = e;code = 101
char = r;code = 114
char = ;code = 32
char = w;code = 119
char = e;code = 101
char = ;code = 32
char = p;code = 112
char = r;code = 114
char = o;code = 111
char = p;code = 112
char = o;code = 111
char = s;code = 115
char = e;code = 101
char = ;code = 32
char = B;code = 66
char = a;code = 97
char = y;code = 121
char = e;code = 101
char = s;code = 115
char = i;code = 105
char = a;code = 97
char = n;code = 110
char = ;code = 32
char = e;code = 101
char = s;code = 115
char = t;code = 116
char = i;code = 105
char = m;code = 109
char = a;code = 97
char = t;code = 116
char = i;code = 105
char = o;code = 111
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char = a;code = 97
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char = ;code = 32
char = a;code = 97
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char = e;code = 101
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char = a;code = 97
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char = i;code = 105
char = v;code = 118
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = o;code = 111
char = ;code = 32
char = N;code = 78
char = H;code = 72
char = S;code = 83
char = T;code = 84
char = ;code = 32
char = i;code = 105
char = n;code = 110
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = a;code = 97
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char = a;code = 97
char = l;code = 108
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char = i;code = 105
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = B;code = 66
char = C;code = 67
char = I;code = 73
char = ;code = 32
char = p;code = 112
char = e;code = 101
char = r;code = 114
char = f;code = 102
char = o;code = 111
char = r;code = 114
char = m;code = 109
char = a;code = 97
char = n;code = 110
char = c;code = 99
char = e;code = 101
char = ;code = 32
char = d;code = 100
char = a;code = 97
char = t;code = 116
char = a;code = 97
char = .;code = 46
char = ;code = 32
char = F;code = 70
char = o;code = 111
char = r;code = 114
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
char = ;code = 32
char = t;code = 116
char = h;code = 104
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char = e;code = 101
char = e;code = 101
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char = m;code = 109
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char = a;code = 97
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char = d;code = 100
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char = i;code = 105
char = g;code = 103
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char = s;code = 115
char = ;code = 32
char = i;code = 105
char = n;code = 110
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char = C;code = 67
char = I;code = 73
char = ;code = 32
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char = e;code = 101
char = a;code = 97
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char = u;code = 117
char = a;code = 97
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char = l;code = 108
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char = a;code = 97
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char = a;code = 97
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char = s;code = 115
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char = ,;code = 44
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char = O;code = 79
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char = g;code = 103
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char = n;code = 110
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char = e;code = 101
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char = ,;code = 44
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char = h;code = 104
char = o;code = 111
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char = h;code = 104
char = a;code = 97
char = t;code = 116
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
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char = e;code = 101
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char = ;code = 32
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char = p;code = 112
char = e;code = 101
char = c;code = 99
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char = a;code = 97
char = l;code = 108
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char = c;code = 99
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char = s;code = 115
char = e;code = 101
char = s;code = 115
char = ;code = 32
char = o;code = 111
char = f;code = 102
char = ;code = 32
char = t;code = 116
char = h;code = 104
char = e;code = 101
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char = h;code = 104
char = i;code = 105
char = e;code = 101
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char = a;code = 97
char = r;code = 114
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char = i;code = 105
char = c;code = 99
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char = g;code = 103
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char = o;code = 111
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char = e;code = 101
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char = ;code = 32
char = (;code = 40
char = H;code = 72
char = G;code = 71
char = L;code = 76
char = M;code = 77
char = );code = 41
char = ,;code = 44
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char = w;code = 119
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char = i;code = 105
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result sql = To statistically evaluate the performance of brain-computer interfaces (BCIs), researchers usually rely on null hypothesis significance testing (NHST), i.e. p-values. However, over-reliance on NHST is often identified as one of the causes of the recent reproducibility crisis in psychology and neuroscience.
In this paper we propose Bayesian estimation as an alternative to NHST in the analysis of BCI performance data. For the three most common experimental designs in BCI research - which would usually be analyzed using a t-test, a linear regression, or an ANOVA - we develop hierarchical models and estimate their parameters using Bayesian inference. Furthermore, we show that the described models are special cases of the hierarchical generalized linear model (HGLM), which we propose as a general framework for the analysis of BCI performance.
We demonstrate the effectiveness of the proposed models on three real datasets and show how the results obtained with Bayesian estimation can give a nuanced insight into BCI performance data. Additionally, we provide all the data and code necessary to reproduce the presented results.
Compared to NHST, Bayesian estimation with the HGLM allows more flexibility in the analysis of BCI performance data from nested experimental designs, and the obtained results have a more straightforward interpretation.
Besides gains in flexibility and interpretability, a wider adoption of the Bayesian estimation approach in BCI studies could bring about greater transparency in data analysis, allow accumulation of knowledge across studies, and reduce questionable practices such as "p-hacking".

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