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ZeroDivisionError fix on f_make (Interactive_Hypothesis_Testing.ipynb) #9

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ZeroDivisionError fix on f_make (Interactive_Hypothesis_Testing.ipynb) #9

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144 changes: 73 additions & 71 deletions Interactive_Hypothesis_Testing.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -229,80 +229,82 @@
"alpha = widgets.FloatSlider(min=0, max = 50, value = 3, step = 1.0, description = '$α$',orientation='horizontal',layout=Layout(width='300px', height='30px'),continuous_update=False)\n",
"alpha.style.handle_color = 'gray'\n",
"\n",
"ui3 = widgets.VBox([L,alpha],) # basic widget formatting \n",
"ui3 = widgets.VBox([L,alpha],) # basic widget formatting \n",
"\n",
"ui4 = widgets.HBox([ui1,ui2,ui3],) # basic widget formatting \n",
"\n",
"ui2 = widgets.VBox([l,ui4],)\n",
"\n",
"def f_make(n1, m1, s1, n2, m2, s2, L, alpha): # function to take parameters, make sample and plot\n",
"def f_make(n1, m1, s1, n2, m2, s2, L, alpha): # function to take parameters, make sample and plot\n",
" #this will prevent a ZeroDivisionError when the number of either sample is 1. \n",
" try: \n",
" np.random.seed(73073)\n",
" x1 = np.random.normal(loc=m1,scale=s1,size=n1)\n",
" np.random.seed(73074)\n",
" x2 = np.random.normal(loc=m2,scale=s2,size=n2)\n",
"\n",
" \n",
" np.random.seed(73073)\n",
" x1 = np.random.normal(loc=m1,scale=s1,size=n1)\n",
" np.random.seed(73074)\n",
" x2 = np.random.normal(loc=m2,scale=s2,size=n2)\n",
" \n",
" mu = (s2*s2)/(s1*s1)\n",
" nu = ((1/n1 + mu/n2)*(1/n1 + mu/n2))/(1/(n1*n1*(n1-1)) + ((mu*mu)/(n2*n2*(n2-1))))\n",
" \n",
" prop_values = np.linspace(-8.0,8.0,100)\n",
" analytical_distribution = stats.t.pdf(prop_values,df = nu) \n",
" analytical_tcrit = stats.t.ppf(1.0-alpha*0.005,df = nu)\n",
" \n",
" # Analytical Method with SciPy\n",
" t_stat_observed, p_value_analytical = stats.ttest_ind(x1,x2,equal_var=False)\n",
" \n",
" # Bootstrap Method\n",
" global_average = np.average(np.concatenate([x1,x2])) # shift the means to be equal to the globla mean\n",
" x1s = x1 - np.average(x1) + global_average\n",
" x2s = x2 - np.average(x2) + global_average\n",
" \n",
" t_stat = np.zeros(L); p_value = np.zeros(L)\n",
" \n",
" random.seed(73075)\n",
" for l in range(0, L): # loop over realizations\n",
" samples1 = random.choices(x1s, weights=None, cum_weights=None, k=len(x1s))\n",
" #print(samples1)\n",
" samples2 = random.choices(x2s, weights=None, cum_weights=None, k=len(x2s))\n",
" #print(samples2)\n",
" t_stat[l], p_value[l] = stats.ttest_ind(samples1,samples2,equal_var=False)\n",
" \n",
" bootstrap_lower = np.percentile(t_stat,alpha * 0.5)\n",
" bootstrap_upper = np.percentile(t_stat,100.0 - alpha * 0.5)\n",
" \n",
" plt.subplot(121)\n",
" #print(t_stat)\n",
" \n",
" plt.hist(x1,cumulative = False, density = True, alpha=0.4,color=\"red\",edgecolor=\"black\", bins = np.linspace(0,50,50), label = '$x_1$')\n",
" plt.hist(x2,cumulative = False, density = True, alpha=0.4,color=\"yellow\",edgecolor=\"black\", bins = np.linspace(0,50,50), label = '$x_2$')\n",
" plt.ylim([0,0.4]); plt.xlim([0.0,30.0])\n",
" plt.title('Sample Distributions'); plt.xlabel('Value'); plt.ylabel('Density')\n",
" plt.legend()\n",
" \n",
" #plt.hist(x2)\n",
" \n",
" plt.subplot(122)\n",
" plt.ylim([0,0.6]); plt.xlim([-8.0,8.0])\n",
" plt.title('Bootstrap and Analytical $t_{statistic}$ Sampling Distributions'); plt.xlabel('$t_{statistic}$'); plt.ylabel('Density')\n",
" plt.plot([t_stat_observed,t_stat_observed],[0.0,0.6],color = 'black',label='observed $t_{statistic}$')\n",
" plt.plot([bootstrap_lower,bootstrap_lower],[0.0,0.6],color = 'blue',linestyle='dashed',label = 'bootstrap interval')\n",
" plt.plot([bootstrap_upper,bootstrap_upper],[0.0,0.6],color = 'blue',linestyle='dashed')\n",
" plt.plot(prop_values,analytical_distribution, color = 'red',label='analytical $t_{statistic}$')\n",
" plt.hist(t_stat,cumulative = False, density = True, alpha=0.2,color=\"blue\",edgecolor=\"black\", bins = np.linspace(-8.0,8.0,50), label = 'bootstrap $t_{statistic}$')\n",
"\n",
" plt.fill_between(prop_values, 0, analytical_distribution, where = prop_values <= -1*analytical_tcrit, facecolor='red', interpolate=True, alpha = 0.2)\n",
" plt.fill_between(prop_values, 0, analytical_distribution, where = prop_values >= analytical_tcrit, facecolor='red', interpolate=True, alpha = 0.2)\n",
" ax = plt.gca()\n",
" handles,labels = ax.get_legend_handles_labels()\n",
" handles = [handles[0], handles[2], handles[3], handles[1]]\n",
" labels = [labels[0], labels[2], labels[3], labels[1]]\n",
"\n",
" plt.legend(handles,labels,loc=1)\n",
" \n",
" \n",
" plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
" plt.show()\n",
" mu = (s2*s2)/(s1*s1)\n",
" nu = ((1/n1 + mu/n2)*(1/n1 + mu/n2))/(1/(n1*n1*(n1-1)) + ((mu*mu)/(n2*n2*(n2-1))))\n",
"\n",
" prop_values = np.linspace(-8.0,8.0,100)\n",
" analytical_distribution = stats.t.pdf(prop_values,df = nu) \n",
" analytical_tcrit = stats.t.ppf(1.0-alpha*0.005,df = nu)\n",
"\n",
" # Analytical Method with SciPy\n",
" t_stat_observed, p_value_analytical = stats.ttest_ind(x1,x2,equal_var=False)\n",
"\n",
" # Bootstrap Method\n",
" global_average = np.average(np.concatenate([x1,x2])) # shift the means to be equal to the globla mean\n",
" x1s = x1 - np.average(x1) + global_average\n",
" x2s = x2 - np.average(x2) + global_average\n",
"\n",
" t_stat = np.zeros(L); p_value = np.zeros(L)\n",
"\n",
" random.seed(73075)\n",
" for l in range(0, L): # loop over realizations\n",
" samples1 = random.choices(x1s, weights=None, cum_weights=None, k=len(x1s))\n",
" #print(samples1)\n",
" samples2 = random.choices(x2s, weights=None, cum_weights=None, k=len(x2s))\n",
" #print(samples2)\n",
" t_stat[l], p_value[l] = stats.ttest_ind(samples1,samples2,equal_var=False)\n",
"\n",
" bootstrap_lower = np.percentile(t_stat,alpha * 0.5)\n",
" bootstrap_upper = np.percentile(t_stat,100.0 - alpha * 0.5)\n",
"\n",
" plt.subplot(121)\n",
" #print(t_stat)\n",
"\n",
" plt.hist(x1,cumulative = False, density = True, alpha=0.4,color=\"red\",edgecolor=\"black\", bins = np.linspace(0,50,50), label = '$x_1$')\n",
" plt.hist(x2,cumulative = False, density = True, alpha=0.4,color=\"yellow\",edgecolor=\"black\", bins = np.linspace(0,50,50), label = '$x_2$')\n",
" plt.ylim([0,0.4]); plt.xlim([0.0,30.0])\n",
" plt.title('Sample Distributions'); plt.xlabel('Value'); plt.ylabel('Density')\n",
" plt.legend()\n",
"\n",
" #plt.hist(x2)\n",
"\n",
" plt.subplot(122)\n",
" plt.ylim([0,0.6]); plt.xlim([-8.0,8.0])\n",
" plt.title('Bootstrap and Analytical $t_{statistic}$ Sampling Distributions'); plt.xlabel('$t_{statistic}$'); plt.ylabel('Density')\n",
" plt.plot([t_stat_observed,t_stat_observed],[0.0,0.6],color = 'black',label='observed $t_{statistic}$')\n",
" plt.plot([bootstrap_lower,bootstrap_lower],[0.0,0.6],color = 'blue',linestyle='dashed',label = 'bootstrap interval')\n",
" plt.plot([bootstrap_upper,bootstrap_upper],[0.0,0.6],color = 'blue',linestyle='dashed')\n",
" plt.plot(prop_values,analytical_distribution, color = 'red',label='analytical $t_{statistic}$')\n",
" plt.hist(t_stat,cumulative = False, density = True, alpha=0.2,color=\"blue\",edgecolor=\"black\", bins = np.linspace(-8.0,8.0,50), label = 'bootstrap $t_{statistic}$')\n",
"\n",
" plt.fill_between(prop_values, 0, analytical_distribution, where = prop_values <= -1*analytical_tcrit, facecolor='red', interpolate=True, alpha = 0.2)\n",
" plt.fill_between(prop_values, 0, analytical_distribution, where = prop_values >= analytical_tcrit, facecolor='red', interpolate=True, alpha = 0.2)\n",
" ax = plt.gca()\n",
" handles,labels = ax.get_legend_handles_labels()\n",
" handles = [handles[0], handles[2], handles[3], handles[1]]\n",
" labels = [labels[0], labels[2], labels[3], labels[1]]\n",
"\n",
" plt.legend(handles,labels,loc=1)\n",
"\n",
"\n",
" plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
" plt.show()\n",
" except ZeroDivisionError:\n",
" print(\"Oops! Recall that you must have more than 1 sample of n1 and n2.\")\n",
"\n",
"\n",
"# connect the function to make the samples and plot to the widgets \n",
Expand Down Expand Up @@ -342,7 +344,7 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "ce2cd3c3c791421b9208affa30d477f8",
"model_id": "bfe242ef0b4f4550afddc52c8fba9394",
"version_major": 2,
"version_minor": 0
},
Expand All @@ -356,12 +358,12 @@
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "46b167d156c74ca5a69dcfca6cb2f270",
"model_id": "5e3b7fc88ca242be9637f233298bdfd0",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
"Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 432x288 with 2 Axes>', 'i…"
]
},
"metadata": {},
Expand Down