Google Data Science interview questions

R1: You need to diagnose an error in the program: The google maps team wants to understand whether dismiss rate is a reasonable metric to help understand user experience of a button in the app. The hypothesis is that, the higher the dismiss rate, the worse the user experience. Hence, they perform a simulation in the A/A comparison scenario. In the simulation, signal = all interactions on the button (click, dismiss, ignore, ...), and negative signal = dismiss. The pseudo code is as follows. Note that we might refer to the numerator and denominator often in later discussions. result_pval = [] for replica in (1:1000):         # the number of overall signals follows a roughly bell shaped distribution         num_signal_control = round(random.normal(150, std = 30))         num_signal_treatment = round(random.normal(150, std = 30))         # given the number of overall signals, the number of negative signals follows a binomial distribution         num_negative_signal_control = random.binomial(num_signal_control, 0.5) num_negative_signal_treatment = random.binomial(num_signal_treatment, 0.5) # define numerator and denominator of the test statistics # the idea of the denominator is: we use Normal approximation to estimate the variance of the numerator p_hat_control = num_negative_signal_control / num_signal_control p_hat_treatment = num_negative_signal_treatment / num_signal_treatment numerator = p_hat_treatment - p_hat_control denominator = sqrt( p_hat_treatment*(1-p_hat_treatment)/num_signal_treatment + p_hat_control *(1-p_hat_control) /num_signal_control ) testing_statistics = numerator / denominator # calculate p value and append to the result vector p_value = 2*std_normal_area_under_curve( lower = abs(testing_statistics), upper = infinity)         result_pval = append(result_pval, p_value) plot_histogram(result_pval) The histogram of the p-values is skewed to the right on [0,1]. In other words, there are more p values < 0.5 than p values > 0.5. Q1: Is such a distribution of p-value expected?

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