Experiments er statistical calculations trial#

In a trial of hypothetical drug 'X' where we are measuring event 'Z', we have two groups. It shows clearly the higher the effect size, the lower sample required for a significant result.The control event rate (CER) is identical to the experimental event rate except that is measured within the scientific control group of an experiment. The probability to determine the difference, if any, is 35%, which is not too low and the probability of missing the desired effect is 65%, which is too high. Add n, remove power pwr.t.test(d=.05, n=2000, sig.level=.05, alternative='two.sided') # Two-sample t test power calculation # n = 2000 # d = 0.05 # sig.level = 0.05 # power = 0.3524674 # alternative = two.sided # NOTE: n is number in *each* group We want to know the probability to get statistically significant results under the mentioned circumstances. In this case, we have an approximate sample size of 4000 visitors and the delta >=5%. Let’s take a look at another case when stakeholders want to get results in a couple of weeks. d - delta, siglevel - confidence level, power - power level pwr.t.test(d=.05, sig.level=.05, power=.9, alternative='two.sided') # Two-sample t test power calculation # n = 8406.896 # d = 0.05 # sig.level = 0.05 # power = 0.9 # alternative = two.sided # NOTE: n is number in *each* group In addition to this, you want to be 90% sure that you will find the differences if they exist, and 95% - that you do not accept the differences that are random fluctuations. This >= 5% gain results in additional profit, which covers all the resources invested in the experiment. Delta, which covers costs of the experiment with a six months return >= 5% gain of the mentioned conversion rate. Let’s assume we test a hypothesis aimed to improve “item to wishlist” conversion rate. Let’s investigate the first case, and use t.test for two independent samples Applying sequential analysis, which allows calculating required sample size during the experiment.Calculating using the confidence level, the effect size, and the power level.There are two approaches to calculating the required sample This level is a consequence of the so-called “one-to-four trade-off” relationship between the levels of α-risk and β-risk: if we accept the significance level α = 0.05, then β = 0.05 × 4 = 0.20 and the power of the criterion is P = 1–0.20 = 0.80. In practice, usually, a test power equal to or greater than 80% is considered acceptable (which corresponds to a β-risk of 20%). By knowing these patterns, we can determine in advance the minimum sample size required to get a statistically significant result. With “sufficiently” large samples, even small differences are statistically significant, and vice versa, with small samples, even large differences are difficult to identify. The most important is the number of observations: the larger the sample size, the higher the statistical power. Also, this analysis makes it possible to estimate the probability of detecting a difference with the given sample size. The power analysis allows you to determine the sample size with a specific confidence level which is required to identify the effect size. Difference magnitude between the samples - Effect size.The higher the power of the statistical test, the less likely you can make a type II error. Statistical power is the probability that one or another statistical criterion can correctly reject the null hypothesis H0, in the case when the alternative hypothesis H1 is true.

Experiments er statistical calculations