Chem Lab Data Analysis
Joe Roith
February 22, 2019
All labs
Descriptive statistics of the individual questions
## # A tibble: 3 x 28
## Treatment Q1mean Q1median Q1sd Q2mean Q2median Q2sd Q3mean Q3median
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Control 4.35 4.00 0.597 3.82 4.00 0.904 3.76 4.00
## 2 Exp Lab 4.21 4.00 0.771 3.94 4.00 0.755 3.67 4.00
## 3 ExpLab* 3.96 4.00 0.475 3.04 3.00 0.706 3.43 4.00
## Q3sd Q4mean Q4median Q4sd Q5mean Q5median Q5sd Q6mean Q6median Q6sd
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.855 4.00 4.00 0.651 4.32 4.00 0.684 3.38 3.00 0.779
## 2 0.953 3.92 4.00 0.846 4.44 4.50 0.616 3.27 3.00 0.610
## 3 0.662 3.91 4.00 0.596 4.00 4.00 0.798 3.04 3.00 0.878
## Q7mean Q7median Q7sd Q8mean Q8median Q8sd Q9mean Q9median Q9sd
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3.88 4.00 0.808 3.59 4.00 0.821 4.06 4.00 0.851
## 2 3.81 4.00 0.938 3.56 4.00 0.796 4.17 4.00 0.883
## 3 3.87 4.00 0.757 3.65 4.00 0.775 3.39 3.00 0.891Descriptives of color groups
## # A tibble: 3 x 10
## Treatment Blue_mean Blue_median Blue_sd Orange_mean Orange_median
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Control 12.2 12.0 1.71 12.2 12.0
## 2 Exp Lab 11.9 12.0 2.06 12.5 12.5
## 3 ExpLab* 11.7 12.0 1.48 10.4 11.0
## Orange_sd Red_mean Red_median Red_sd
## <dbl> <dbl> <dbl> <dbl>
## 1 2.24 10.7 11.0 2.14
## 2 1.98 10.5 11.0 1.91
## 3 1.80 10.1 10.0 2.07Plots of all questions
Plots of question color
Just Professor 1 and 2
T-tests
Remember, a smaller p-value indicates stronger evidence that there is a difference in the groups. We typically need p-value to be less than 0.05 to be convinced there’s significant difference.
All questions: No significant difference
##
## Welch Two Sample t-test
##
## data: Score by Treatment
## t = 0.2371, df = 218.22, p-value = 0.8128
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4809315 0.6124675
## sample estimates:
## mean in group Control mean in group Exp Lab
## 11.72549 11.65972Blue questions: No significant difference
##
## Welch Two Sample t-test
##
## data: BlueTotal by Treatment
## t = 0.71433, df = 77.92, p-value = 0.4772
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.532172 1.127760
## sample estimates:
## mean in group Control mean in group Exp Lab
## 12.23529 11.93750Orange questions: No significant difference
##
## Welch Two Sample t-test
##
## data: OrangeTotal by Treatment
## t = -0.70156, df = 65.499, p-value = 0.4854
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.2915228 0.6199542
## sample estimates:
## mean in group Control mean in group Exp Lab
## 12.20588 12.54167Red questions: No significant difference
##
## Welch Two Sample t-test
##
## data: RedTotal by Treatment
## t = 0.51287, df = 66.148, p-value = 0.6098
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.6806567 1.1512449
## sample estimates:
## mean in group Control mean in group Exp Lab
## 10.73529 10.50000Just Professor 1
All questions: No significant difference
##
## Welch Two Sample t-test
##
## data: Score by Treatment
## t = 0.2371, df = 218.22, p-value = 0.8128
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.4809315 0.6124675
## sample estimates:
## mean in group Control mean in group Exp Lab
## 11.72549 11.65972Blue questions: No significant difference
##
## Welch Two Sample t-test
##
## data: BlueTotal by Treatment
## t = -0.56273, df = 57.9, p-value = 0.5758
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.1021668 0.6184712
## sample estimates:
## mean in group Control mean in group Exp Lab
## 11.69565 11.93750Orange questions: No significant difference
##
## Welch Two Sample t-test
##
## data: OrangeTotal by Treatment
## t = -1.2971, df = 41.66, p-value = 0.2017
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.7180578 0.3738549
## sample estimates:
## mean in group Control mean in group Exp Lab
## 11.86957 12.54167Red questions: No significant difference
##
## Welch Two Sample t-test
##
## data: RedTotal by Treatment
## t = -1.0417, df = 44.095, p-value = 0.3032
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.4672996 0.4672996
## sample estimates:
## mean in group Control mean in group Exp Lab
## 10.0 10.5ANOVA for Color Total and all three treatment groups
Orange actually is significant, this is visualized in the histogram above with all treatments which shows the ExpLab* with lower scores overall. Also in the boxplots below (with mean score).
## Df Sum Sq Mean Sq F value Pr(>F)
## Treatment 2 71.8 35.89 8.694 0.000326 ***
## Residuals 102 421.1 4.13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Blue is not significant
## Df Sum Sq Mean Sq F value Pr(>F)
## Treatment 2 3.6 1.813 0.539 0.585
## Residuals 102 343.4 3.366
Red is not significant
## Df Sum Sq Mean Sq F value Pr(>F)
## Treatment 2 5.0 2.511 0.614 0.543
## Residuals 102 417.2 4.090