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Statistical / Analysis Knowledge, Probability knowledge - Coggle Diagram

- - - - \(\fbox{Definition}\): A/B testing is utilized to compare the performance of 2 products against each other and decide which product is better.
      - \(\fbox{procedure}\)
    - - Chi-square Pearson test
        
        \(\fbox{application}\): test out the relation between the label and the input feature. Essentially, it's all about whether the label and the input feature is independent ir dependent
        
        \(\fbox{procedure}\): 1. null and alternative hypotheses about dependency . 2. observed and expected contingency table. The expected frequency is calculated by (row total * column total )/grand total while the degree-of-freedom is (#rows-1)(#columns-1) 3. Calculate the chi-square value, and figure out the p-value. Compare the p-value with alpha to see whether it has a significant level of alpha
        
        Condition: the data are randomly selected from a population
      - contingency table：the table in matrix form to display the frequency distribution of the variables.
    - - \(\fbox{Definition}\): check if the samples / model are different from each other.
      - \(\fbox{comparison}\): t-test have the same idea as ANOVA. However, in the case with more than 2 samples, it's better to apply ANOVA rather than t-test.
      - procedure
        
        \(\fbox{procedure(sample)}\): 1.Make the hypotheses on the sample mean.NULL: same mean. 2. Calculate the grand mean, sample mean, within group variability, between group variability 3. Carry out the F-test by calculating the F-statistics and determine the p-value.
        
        \(\fbox{procedure(model)}\): Call the avova function to check mutual independence model. if the p-value is say larger than 0.05, it means the simpler model is an alternative model.
        
        AIC / BIC: negarive likelihood +plus penalty (number of parameters in the model). the Smaller AIC/BIC the better the model is.
      - type
        
        One-way Anova: #COVID cases vs. country
        
        two-way ANOVA: #cases vs. country&gender
        
        N-way ANOVA: #COVID cases vs. xxxxxxx
- - - - ARMA(Autoregressive moving average)
      - AR(Autoregression)
      - MA(Moving Average): sum of iid white Noise
      - ARIMA (Autoregressive Integrated moving average): ARIMA(p,d,q) where d is the number of defferencing steps to make the series stationary
    - - approach
        
        Eliminating trend and seasonality by differencing: take the difference between a particular time lag
        
        Decomposition: modeling Bothe the trend and seasonality, then remove them from the model
    - - ARIMA(p,d,q)
      - model selection: the model with smallest AIC and BIC value.
        
        \(\fbox{procedure}\): 1.Choose the model with smallest AIC and BIC value. 2.check the residual of series-ARIMA model, see if the residual is iid white Noise by hypotheses testing (some sorts of chi-square test)
    - - residual plot: ACF (auto-correlation plot) / PACF (partial auto-correlation plot): partial correlation of a stationary time series.