PR by melviii100

build.py

@@ -1,4 +1,147 @@
+from __future__ import division   # Get float values for all division operations.
+from scipy import stats
 
+'''
+    Assumptions:
+        The populations from which the samples were obtained must be normally or approximately normally distributed.
+        The samples must be independent.
+        The variances of the populations must be equal.
 
-def solution(set1, set2, set3, p_level):
-    pass
+    Hypotheses
+        The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different.
+
+    Decision Rule :
+        The decision will be to reject the null hypothesis if the test statistic from the table is greater than
+        the F critical value with k-1 numerator and N-k denominator degrees of freedom.
+
+        If the decision is to reject the null, then at least one of the means is different.
+        However, the ANOVA does not tell you where the difference lies. For this, you need another test, either the Scheffe' or Tukey test.
+
+        F Value/F Ratio in One Way ANOVA: When to Reject the Null :
+            The F Value in ANOVA
+                The F value (also called an F statistic or F Ratio) in one way ANOVA is a tool to help you answer
+                the question "Is the variance between the means of two populations significantly different?""
+                The F value in the ANOVA test also determines the P value; The P value is the probability of getting a result at least as extreme as the one that was actually observed, given that the null hypothesis is true.
+
+            Reject the null when your p value is smaller than your alpha level.
+            You should not reject the null if your critical f value is smaller than your F Value,
+            unless you also have a small p-value.
+
+            Where this could get confusing is where one of these values seems to indicate that you should
+            reject the null hypothesis and one of the values indicates you should not. For example,
+            let's say your One Way ANOVA has a p value of 0.68 and an alpha level of 0.05. As the p value is large,
+            you should not reject the null hypothesis. However, your f value is 0.40 with an f critical value of 3.2.
+            Should you now reject the null hypothesis? The answer is NO.
+
+            Why?
+                The F value should always be used along with the p value in deciding whether your results
+                are significant enough to reject the null hypothesis. If you get a large f value
+                (one that is bigger than the F critical value found in a table), it means something is significant,
+                while a small p value means all your results are significant. The F statistic just compares the
+                joint effect of all the variables together.
+
+                To put it simply, reject the null hypothesis only if your alpha level is larger than your p value.
+
+'''
+
+
+def solution(set1, set2, set3, probability_level):
+
+    placebo  = set1
+    low_dose = set2
+    moderate_dose = set3
+
+    # +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+    								# Method 1
+
+    f_statistic_or_f_value, p_value = stats.f_oneway(placebo, low_dose, moderate_dose)
+    print(f_statistic_or_f_value, p_value )
+
+    # +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+    								# Mthod 2
+
+    # Calculating using Python (i.e., pure Python ANOVA)
+    n = len(placebo)  	# Number of items in sample. Here all samples has equal length. If it has different length, different method has to follow.
+    k = 3  				# Number of independent groups
+    N = len(placebo) + len(low_dose) + len(moderate_dose)  # N is the total sample size.
+
+
+    T1 = sum(placebo)
+    T2 = sum(low_dose)
+    T3 = sum(moderate_dose)
+
+    T1_square = T1**2
+    T2_square = T2**2
+    T3_square = T3**2
+
+    GT = T1 + T2 + T3 	# Grand Total
+
+    # SSwithin
+    sum_placebo_square = sum([x**2 for x in placebo])
+    sum_low_does_square =  sum([x**2 for x in low_dose])
+    sum_moderate_dose_square = sum([x**2 for x in moderate_dose])
+
+    SSwithin = (sum_placebo_square - T1_square / n) + (sum_low_does_square - T2_square / n) + (sum_moderate_dose_square - T3_square / n)
+
+
+    # SSbetween
+    SSbetween = ((T1_square / n) + (T2_square / n) + (T3_square / n)) - (GT**2 / N)
+
+    # SSTotal
+    SSTotal_original = (sum_placebo_square + sum_low_does_square + sum_moderate_dose_square) - (GT**2 / N )
+    SSTotal = SSbetween + SSwithin
+    if round(SSTotal_original,5) != round(SSTotal, 5):
+    	print("Error in calculation")
+    	exit(-1)
+
+    print(SSTotal_original, SSTotal)
+
+    # ------------------------------------
+    DFbetween = k - 1
+    DFwithin = N - k
+
+    # ------------------------------------
+    MSbetween = SSbetween/DFbetween
+    MSwithin = SSwithin/DFwithin
+
+    # ------------------------------------
+    # Calculating the F-value
+    f_statistic_or_f_value = MSbetween/MSwithin
+
+    '''
+    	To reject the null hypothesis we check if the obtained F-value is above the critical value for rejecting the null hypothesis.
+    	We could look it up in a F-value table based on the DFwithin and DFbetween. However, there is a method in SciPy for obtaining a p-value.
+    '''
+
+    # ------------------------------------
+    # Calculate p value
+    p_value = stats.f.sf(f_statistic_or_f_value, DFbetween, DFwithin)
+
+    print(f_statistic_or_f_value, p_value )
+
+    # ------------------------------------
+    # Finally, we are also going to calculate effect size. We start with the commonly used eta-squared :
+    eta_sqrd = SSbetween/SSTotal
+
+    '''
+     	However, eta-squared is somewhat biased because it is based purely on sums of squares from the sample.
+     	No adjustment is made for the fact that what we aiming to do is to estimate the effect size in the population.
+     	Thus, we can use the less biased effect size measure Omega squared:
+    '''
+    om_sqrd = (SSbetween - (DFbetween * MSwithin))/(SSTotal + MSwithin)
+    om_sqrd = (SSbetween - (DFbetween * MSwithin))/(SSTotal + MSwithin)
+
+    print(eta_sqrd, om_sqrd)
+
+
+    # +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+    '''
+    	Decision Rule :
+    		The decision will be to reject the null hypothesis if the test statistic from the table is greater than
+    		the F critical value with k-1 numerator and N-k denominator degrees of freedom.
+    '''
+
+    if probability_level > p_value:
+        return True
+
+    return False