small text things, cleaned up FDR/q-value defs

Author: mahort

Lecture-2-Linear-Regression.ipynb

@@ -564,7 +564,7 @@
    "source": [
     "Your data will often deviate from a normal distribution (sometimes drastically, like Cadmium Chloride shown above).\n",
     "However, one of the assumptions of the model that we use in GWAS is that the residuals are normally distrbuted.\n",
-    "Violations of this assumption can result in model misspecification and thus biased parameter estimates."
+    "Violations of this assumption can result in model misspecification and biased parameter estimates."
    ]
   },
   {
@@ -578,7 +578,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "There are a wide variety of methods to stabilize variance and make data normally distributed. Here, we explore the usefulness of the Box-Cox transformation as well as a (non-parametric) rank-based transformation."
+    "There are a wide variety of methods to stabilize variance and make data normally distributed. Here, we explore the Box-Cox transformation as well as a (non-parametric) rank-based transformation."
    ]
   },
   {
@@ -615,7 +615,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The rank transformation normalizes the data by converting the data to ranks and then transforming these ranks to the corresponding quantiles of a normal distribution. Because this transformation does not rely on a parameter (or actually one parameter per sample, namely the normal quantile), it is called non-parametric.\n",
+    "The rank transformation normalizes the data by converting the data to ranks and then transforming these ranks to the corresponding quantiles of a normal distribution. Because this transformation does not rely on or specify a parameter it is considered non-parametric.\n",
     "\n",
     "Before using a rank-based transformation, you should consider whether other models (e.g. the binomial model) are more appropriate for your data."
    ]
@@ -831,7 +831,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Next, we convert the P-values to a pandas DataFrame:"
+    "Next, we convert the P-values into a pandas DataFrame:"
    ]
   },
   {
@@ -1532,9 +1532,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "False discovery rates (FDR) give an idea of the expected type-1 error rate at a given P-value threshold. If we are testing millions of hypotheses, then we might be willing to accept type-1 errors at a given rate, if in return we get more discoveries.\n",
+    "False discovery rates (FDR) give an idea of the expected type-1 error rate at a given *P*-value threshold. This measure gives a useful alternative to traditional Bonferroni correction, which bounds the so-called family-wise error rate (FWER), namely the probability of having at least a single type-1 error.\n",
     "\n",
-    "This measure gives a useful alternative to traditional Bonferroni correction, which bounds the so-called family-wise error rate (FWER), namely the probability of having at least a single type 1 error."
+    "That is, a *P* value is the rate at which truly null hypotheses are called significant.\n",
+    "\n",
+    "The FDR is the rate that which significant results are truly null. So an FDR rate of 5% means that - among all of the features that are called significant - 5% of these will be false positives."
    ]
   },
   {
@@ -1548,7 +1550,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Definition: minimum false discovery rate threshold that would allow the variable to be significant."
+    "These are, like _P_ values, a measure of significance for a given test. \n",
+    "\n",
+    "In practice, if one is willing to accept a result at an FDR of the given $q$ value (e.g. 0.03) then among the results that have a lower $q$ value, $q$ percent of those will be false positives (3% in this example)."
    ]
   },
   {
@@ -1638,7 +1642,7 @@
     {
      "data": {
       "text/plain": [
-       "<matplotlib.legend.Legend at 0x1a24e668d0>"
+       "<matplotlib.legend.Legend at 0x1a23b30290>"
       ]
      },
      "execution_count": 25,