data pattern: How many choices people made?

## Number of people who made one choice: 65 ( 38.69 %)
## Number of people who made two choices: 99 ( 58.93 %)
## Number of people who made more than two choices: 4 ( 2.381 %)
## Total number of unique users: 168

data pattern: How many checked at clinical result text or image when it is present (for those product that is chosen)

## How many chosen product's clinical image is checked out: 10 ( 12.99 %)
## How many chosen product's clinical results is checked out: 5 ( 6.49 %)
## How many chosen product's clinical results/images is checked out: 15 ( 19.48 %)

data pattern: How many checked at clinical result text or image when it is present (for all interacted user-product pair)

## Proportion of people who checked the product page: 66 out of 170 ( 38.82 %)
## Of people in the treatment group who checked product pages, 15 out of 32 ( 46.88 %) also viewed clinical results/images
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##     1.0     1.0     2.0     2.3     2.0    15.0
## Standard Deviation: 1.99

Proportion that choose Group I product (with claim in treatment condition)

## # A tibble: 2 × 7
##   Group         n mean_treatment_pa sd_treatment_pa se_treatment_pa ci_lower
##   <chr>     <int>             <dbl>           <dbl>           <dbl>    <dbl>
## 1 Control     136             0.544           0.500          0.0429    0.459
## 2 Treatment   128             0.602           0.492          0.0434    0.516
## # ℹ 1 more variable: ci_upper <dbl>
## 
##  Welch Two Sample t-test
## 
## data:  treatment_pa by Group
## t = -0.94125, df = 261.5, p-value = 0.3474
## alternative hypothesis: true difference in means between group Control and group Treatment is not equal to 0
## 95 percent confidence interval:
##  -0.17761857  0.06272886
## sample estimates:
##   mean in group Control mean in group Treatment 
##               0.5441176               0.6015625

The sample size needed for each group is 1646

## # A tibble: 2 × 7
##   Group         n mean_treatment_pa sd_treatment_pa se_treatment_pa ci_lower
##   <chr>     <int>             <dbl>           <dbl>           <dbl>    <dbl>
## 1 Control      85             0.518           0.503          0.0545    0.409
## 2 Treatment    79             0.570           0.498          0.0561    0.458
## # ℹ 1 more variable: ci_upper <dbl>
## 
##  Welch Two Sample t-test
## 
## data:  treatment_pa by Group
## t = -0.66461, df = 161.32, p-value = 0.5073
## alternative hypothesis: true difference in means between group Control and group Treatment is not equal to 0
## 95 percent confidence interval:
##  -0.2064038  0.1024574
## sample estimates:
##   mean in group Control mean in group Treatment 
##               0.5176471               0.5696203

### The sample size needed for each group is 4225 when only use the first choice

## [1] "Treatment analysis for users who checked product page:"
## # A tibble: 2 × 7
##   Group         n mean_treatment_pa sd_treatment_pa se_treatment_pa ci_lower
##   <chr>     <int>             <dbl>           <dbl>           <dbl>    <dbl>
## 1 Control      35             0.543           0.505          0.0854    0.369
## 2 Treatment    31             0.710           0.461          0.0829    0.540
## # ℹ 1 more variable: ci_upper <dbl>
## 
##  Welch Two Sample t-test
## 
## data:  treatment_pa by Group
## t = -1.4016, df = 63.934, p-value = 0.1659
## alternative hypothesis: true difference in means between group Control and group Treatment is not equal to 0
## 95 percent confidence interval:
##  -0.40460322  0.07096267
## sample estimates:
##   mean in group Control mean in group Treatment 
##               0.5428571               0.7096774

### The sample size needed for each group is 143 when only consider choices that product page clicked

##            Variable               Test Statistic P_Value Significant
## D   claim_benchmark Kolmogorov-Smirnov    0.0781  0.7265          No
## W   claim_benchmark  Wilcoxon Rank-Sum 2215.5000  0.9618          No
## D1   lottery_choice Kolmogorov-Smirnov    0.0606  0.3625          No
## W1   lottery_choice  Wilcoxon Rank-Sum 2361.5000  0.3490          No
## D2 avg_awareness_pa Kolmogorov-Smirnov    0.1526  0.2704          No
## W2 avg_awareness_pa  Wilcoxon Rank-Sum 2341.0000  0.8387          No
## D3   avg_loyalty_pa Kolmogorov-Smirnov    0.2332  0.0277         Yes
## W3   avg_loyalty_pa  Wilcoxon Rank-Sum 2241.0000  0.8182          No
## D4   avg_quality_pa Kolmogorov-Smirnov    0.1155  0.5601          No
## W4   avg_quality_pa  Wilcoxon Rank-Sum 2297.0000  0.9913          No
## D5           Rating Kolmogorov-Smirnov    0.2480  0.0166         Yes
## W5           Rating  Wilcoxon Rank-Sum 2376.0000  0.7215          No
## D6          Reviews Kolmogorov-Smirnov    0.3112  0.0013         Yes
## W6          Reviews  Wilcoxon Rank-Sum 2537.0000  0.2889          No
## D7          h_price Kolmogorov-Smirnov    0.3108  0.0010         Yes
## W7          h_price  Wilcoxon Rank-Sum 2649.0000  0.1207          No
## # A tibble: 2 × 25
##   treatment_pa claim_benchmark_mean claim_benchmark_median claim_benchmark_sd
##          <dbl>                <dbl>                  <dbl>              <dbl>
## 1            0                 4.69                      5               1.47
## 2            1                 4.67                      5               1.55
## # ℹ 21 more variables: lottery_choice_mean <dbl>, lottery_choice_median <dbl>,
## #   lottery_choice_sd <dbl>, avg_awareness_pa_mean <dbl>,
## #   avg_awareness_pa_median <dbl>, avg_awareness_pa_sd <dbl>,
## #   avg_loyalty_pa_mean <dbl>, avg_loyalty_pa_median <dbl>,
## #   avg_loyalty_pa_sd <dbl>, avg_quality_pa_mean <dbl>,
## #   avg_quality_pa_median <dbl>, avg_quality_pa_sd <dbl>, Rating_mean <dbl>,
## #   Rating_median <dbl>, Rating_sd <dbl>, Reviews_mean <dbl>, …