experiments and inference

t检验，AB-test

t检验的条件：
完全随机分组
服从正态分布，两组方差一致（方差齐性检验，服从F分布）


要得到观测到的两组区别（MDE）（销量上的差异、单店毛利的差异），在显著性水平为10%（alpha）,统计效力为80%的情况下，样本要达到多少；

PSM

Propensity Score Matching (PSM) is a statistical technique used to reduce selection bias in observational studies where random assignment is not feasible. It aims to create a control group that is statistically similar to the treatment group based on observed covariates.

Here’s how PSM works:

1. Estimate Propensity Scores: The first step is to estimate the propensity scores using a logistic regression model (or another appropriate model). The propensity score is the probability of a unit (e.g., a person) receiving the treatment given their covariates. The model predicts the likelihood of being assigned to the treatment group based on observed characteristics.

2. Match Units: Units in the treatment group are matched with units in the control group that have similar propensity scores. There are several methods for matching:

   • Nearest neighbor matching: Each treated unit is matched with the control unit with the closest propensity score.
   • Caliper matching: Matches are only made if the propensity scores are within a certain range (caliper).
   • Stratification (or subclassification): The sample is divided into strata based on propensity scores, and comparisons are made within each stratum.
   • Radius matching: Each treated unit is matched with all control units within a specified radius of the propensity score.
   • Kernel matching: All treated units are matched with a weighted average of all control units, with weights inversely proportional to the distance between propensity scores.

3. Check Balance: After matching, it’s important to check the balance of covariates between the treatment and control groups to ensure that they are similar. This can be done using standardized mean differences or other diagnostic tools.

4. Estimate Treatment Effect: The treatment effect is estimated by comparing the outcomes of the matched treatment and control units. Common estimators include the Average Treatment Effect on the Treated (ATT) and the Average Treatment Effect (ATE).