Data Attrition
## [1] "Original dataset has 231 rows"
## Condition Rows_Remaining Rows_Discarded
## 1 2. Do not consent 228 3
## 2 3. Tech_screener failed 205 23
## 3 4. Not in the US 205 0
## 4 5. Not Female 198 7
## 5 6. Use cream less than 3 times a week 171 27
## 6 7. Fail attention check 170 1
## 7 TOTAL 170 61
## [1] "Percentage of records kept: 73.59 %"
## [1] "Percentage of records discarded: 26.41 %"
## [1] "Final filtered dataset (df_cp) dimensions: 170 rows x 80 columns"
Survey - product choice
## Column Non_NA_Count Percent_Complete
## age...22 age...22 165 100.00
## use_frequency use_frequency 165 100.00
## edu edu 165 100.00
## race...57 race...57 165 100.00
## income income 165 100.00
## employ employ 165 100.00
## purchase_frequency purchase_frequency 165 100.00
## purchase_amount purchase_amount 165 100.00
## importance importance 165 100.00
## participantId participantId 165 100.00
## Mec_benchmark_1 Mec_benchmark_1 36 21.82
## Mec_study_effet_b_1 Mec_study_effet_b_1 23 13.94
## Mec_clinical_study_b_1 Mec_clinical_study_b_1 20 12.12
## Mec_clinical_study_a_1 Mec_clinical_study_a_1 14 8.48
## disclaimer_1_b_1 disclaimer_1_b_1 14 8.48
## disclaimer_3_b_1 disclaimer_3_b_1 14 8.48
## Mec_study_effet_a_1 Mec_study_effet_a_1 13 7.88
## disclaimer_2_b_1 disclaimer_2_b_1 12 7.27
## disclaimer_1_a_1 disclaimer_1_a_1 7 4.24
## disclaimer_2_a_1 disclaimer_2_a_1 6 3.64
## disclaimer_3_a_1 disclaimer_3_a_1 6 3.64
The proportion that choose 1
## [1] "Proportions of Value = 1 with 95% Confidence Intervals:"
## Column Proportion Count Total SE CI_Lower CI_Upper
## 1 Mec_benchmark_1 0.4444444 16 36 0.08281733 0.2821225 0.6067664
## 2 Mec_study_effet_b_1 0.6521739 15 23 0.09931135 0.4575237 0.8468242
## 3 Mec_clinical_study_b_1 0.8500000 17 20 0.07984360 0.6935065 1.0000000
## 4 disclaimer_1_b_1 0.7142857 10 14 0.12073632 0.4776425 0.9509289
## 5 disclaimer_2_b_1 0.9166667 11 12 0.07978559 0.7602869 1.0000000
## 6 disclaimer_3_b_1 0.8571429 12 14 0.09352195 0.6738398 1.0000000
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.444)
## - Mec_study_effet_b_1 (p2 = 0.652)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 88.90845
## p1 = 0.4444444
## p2 = 0.6521739
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.444)
## - Mec_clinical_study_b_1 (p2 = 0.850)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 20.57188
## p1 = 0.4444444
## p2 = 0.85
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.444)
## - disclaimer_1_b_1 (p2 = 0.714)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 51.34368
## p1 = 0.4444444
## p2 = 0.7142857
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_study_effet_b_1 (p1 = 0.652)
## - Mec_clinical_study_b_1 (p2 = 0.850)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 73.80086
## p1 = 0.6521739
## p2 = 0.85
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_b_1 (p1 = 0.850)
## - disclaimer_1_b_1 (p2 = 0.714)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 144.0414
## p1 = 0.85
## p2 = 0.7142857
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_b_1 (p1 = 0.850)
## - disclaimer_2_b_1 (p2 = 0.917)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 362.8106
## p1 = 0.85
## p2 = 0.9166667
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_b_1 (p1 = 0.850)
## - disclaimer_3_b_1 (p2 = 0.857)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 38454.41
## p1 = 0.85
## p2 = 0.8571429
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
The proportion that choose 2
## [1] "Proportions of Value = 2 with 95% Confidence Intervals:"
## Column Proportion Count Total SE CI_Lower CI_Upper
## 1 Mec_benchmark_1 0.5555556 20 36 0.08281733 0.39323358 0.7178775
## 2 Mec_study_effet_a_1 0.3846154 5 13 0.13493200 0.12014866 0.6490821
## 3 Mec_clinical_study_a_1 0.6428571 9 14 0.12806021 0.39185913 0.8938552
## 4 disclaimer_1_a_1 0.5714286 4 7 0.18704391 0.20482252 0.9380346
## 5 disclaimer_2_a_1 0.6666667 4 6 0.19245009 0.28946449 1.0000000
## 6 disclaimer_3_a_1 0.5000000 3 6 0.20412415 0.09991668 0.9000833
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.556)
## - Mec_study_effet_a_1 (p2 = 0.385)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 132.6383
## p1 = 0.5555556
## p2 = 0.3846154
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.556)
## - Mec_clinical_study_a_1 (p2 = 0.643)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 493.461
## p1 = 0.5555556
## p2 = 0.6428571
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_benchmark_1 (p1 = 0.556)
## - disclaimer_1_a_1 (p2 = 0.571)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 15323.76
## p1 = 0.5555556
## p2 = 0.5714286
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_study_effet_a_1 (p1 = 0.385)
## - Mec_clinical_study_a_1 (p2 = 0.643)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 57.60947
## p1 = 0.3846154
## p2 = 0.6428571
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_a_1 (p1 = 0.643)
## - disclaimer_1_a_1 (p2 = 0.571)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 732.6902
## p1 = 0.6428571
## p2 = 0.5714286
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_a_1 (p1 = 0.643)
## - disclaimer_2_a_1 (p2 = 0.667)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 6258.303
## p1 = 0.6428571
## p2 = 0.6666667
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study_a_1 (p1 = 0.643)
## - disclaimer_3_a_1 (p2 = 0.500)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 187.1898
## p1 = 0.6428571
## p2 = 0.5
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
Combine both
## Column Proportion SE CI_Lower CI_Upper Count Total Label
## 1 Benchmark 0.4444444 0.08281733 0.2821225 0.6067664 16 36 Benchmark
## 2 Mec_study_effet 0.5555556 0.08281733 0.3932336 0.7178775 20 36 Study
## 3 Mec_clinical_study 0.7647059 0.07274670 0.6221224 0.9072894 26 34 Clinical Study
## 4 disclaimer_clinical 0.6666667 0.10286890 0.4650436 0.8682897 14 21 Clinical Disclaimer
## 5 disclaimer_degree 0.8333333 0.08784105 0.6611649 1.0000000 15 18 Degree Disclaimer
## 6 disclaimer_consumer 0.7500000 0.09682458 0.5602238 0.9397762 15 20 Consumer Disclaimer
## Power analysis to detect difference between:
## - Benchmark (p1 = 0.444)
## - Mec_study_effet (p2 = 0.556)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 316.6981
## p1 = 0.4444444
## p2 = 0.5555556
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Benchmark (p1 = 0.444)
## - Mec_clinical_study (p2 = 0.765)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 35.38599
## p1 = 0.4444444
## p2 = 0.7647059
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Benchmark (p1 = 0.444)
## - disclaimer_clinical (p2 = 0.667)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 77.29929
## p1 = 0.4444444
## p2 = 0.6666667
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_study_effet (p1 = 0.556)
## - Mec_clinical_study (p2 = 0.765)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 79.3231
## p1 = 0.5555556
## p2 = 0.7647059
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study (p1 = 0.765)
## - disclaimer_clinical (p2 = 0.667)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 331.1402
## p1 = 0.7647059
## p2 = 0.6666667
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study (p1 = 0.765)
## - disclaimer_degree (p2 = 0.833)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 534.0651
## p1 = 0.7647059
## p2 = 0.8333333
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
## Power analysis to detect difference between:
## - Mec_clinical_study (p1 = 0.765)
## - disclaimer_consumer (p2 = 0.750)
## Required sample size per group to detect this difference with 80% power (α = 0.05):
##
##
## Two-sample comparison of proportions power calculation
##
## n = 13337.99
## p1 = 0.7647059
## p2 = 0.75
## sig.level = 0.05
## power = 0.8
## alternative = two.sided
##
## NOTE: n is number in *each* group
Consensus and magnitude confusion
## [1] "Mean values with 95% confidence intervals for confidence degree variables:"
## Column Mean SD SE CI_Lower CI_Upper n
## 1 Con-degree-high 2.843373 1.0179119 0.11173034 2.624382 3.062365 83
## 2 Con-degree-low 2.609756 0.7818323 0.08633893 2.440532 2.778980 82
## Basic statistics:
## Con-degree-high: Mean = 2.843373 , SD = 1.017912 , n = 83
## Con-degree-low: Mean = 2.609756 , SD = 0.7818323 , n = 82
## Difference (high - low): 0.2336174
## One-sided t-test (Con-degree-high > Con-degree-low):
##
## Welch Two Sample t-test
##
## data: high_confidence and low_confidence
## t = 1.6545, df = 153.69, p-value = 0.05003
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## -4.814539e-05 Inf
## sample estimates:
## mean of x mean of y
## 2.843373 2.609756
##
## Hypothesis Test Summary:
## -------------------------
## Null Hypothesis: Mean of Con-degree-high is less than or equal to mean of Con-degree-low
## Alternative Hypothesis: Mean of Con-degree-high is greater than mean of Con-degree-low
## Test statistic (t): 1.654
## Degrees of freedom: 153.691
## p-value: 0.05003
## Decision: Fail to reject the null hypothesis at the 0.05 significance level.
## Conclusion: There is insufficient evidence to conclude that the mean of Con-degree-high
## is significantly greater than the mean of Con-degree-low.
##
## Effect size (Cohen's d): 0.257
## Interpretation: Medium effect size
