Question 1

H0: All 3 means will be equal. HA: At least one of the means will be different.

## Call:
##    aov(formula = Baumann$post.test.3 ~ Baumann$group)
## 
## Terms:
##                 Baumann$group Residuals
## Sum of Squares        357.303  2511.682
## Deg. of Freedom             2        63
## 
## Residual standard error: 6.314108
## Estimated effects may be unbalanced
## Analysis of Variance Table
## 
## Response: Baumann$post.test.3
##               Df Sum Sq Mean Sq F value  Pr(>F)  
## Baumann$group  2  357.3 178.652  4.4811 0.01515 *
## Residuals     63 2511.7  39.868                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The anova shows that there is some difference in the teaching styles somewhere that is affecting the results of post.test.3. Because of this, we reject the null hypothesis and accept the alternate.

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  Baumann$post.test.3 and Baumann$group 
## 
##       Basal DRTA 
## DRTA  0.012 -    
## Strat 0.285 0.606
## 
## P value adjustment method: bonferroni
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Baumann$post.test.3 ~ Baumann$group)
## 
## $`Baumann$group`
##                  diff       lwr       upr     p adj
## DRTA-Basal   5.681818  1.112137 10.251499 0.0111135
## Strat-Basal  3.227273 -1.342408  7.796953 0.2149995
## Strat-DRTA  -2.454545 -7.024226  2.115135 0.4064363

One of three dependent variables have means that are significantly different. This is identified by DRTA-Basal having a p-value that is less than .05. This shows that teaching style does have an impact on the results of students.

##               Df   Wilks approx F num Df den Df    Pr(>F)    
## Baumann$group  2 0.63202   5.2433      6    122 7.774e-05 ***
## Residuals     63                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##               Df  Pillai approx F num Df den Df    Pr(>F)    
## Baumann$group  2 0.40825   5.3005      6    124 6.765e-05 ***
## Residuals     63                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##               Df Hotelling-Lawley approx F num Df den Df    Pr(>F)    
## Baumann$group  2          0.51852   5.1852      6    120 8.949e-05 ***
## Residuals     63                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##               Df     Roy approx F num Df den Df    Pr(>F)    
## Baumann$group  2 0.31845   6.5813      3     62 0.0006206 ***
## Residuals     63                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The test statistics back that there are differences in the performance of the teaching styles.

Even when looking at the boxplots of the results of post.test.3, you can see the differences in the results of each teaching method.

Question 2

H0: All means will be the same for the post-tests. HA: At least one of the means will be different in the post-tests.

##  Response post.test.1 :
##               Df Sum Sq Mean Sq F value   Pr(>F)   
## Baumann$group  2 108.12  54.061  5.3174 0.007347 **
## Residuals     63 640.50  10.167                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response post.test.2 :
##               Df Sum Sq Mean Sq F value    Pr(>F)    
## Baumann$group  2  95.12  47.561   8.407 0.0005804 ***
## Residuals     63 356.41   5.657                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response post.test.3 :
##               Df Sum Sq Mean Sq F value  Pr(>F)  
## Baumann$group  2  357.3 178.652  4.4811 0.01515 *
## Residuals     63 2511.7  39.868                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Each of the post.test results have significant values showing that there are differences in each results based on the teaching method used.

## 
##  Descriptive statistics by group 
## group: Basal
##             vars  n  mean   sd median trimmed  mad min max range skew kurtosis
## group*         1 22  1.00 0.00    1.0    1.00 0.00   1   1     0  NaN      NaN
## post.test.1    2 22  6.68 2.77    6.5    6.56 2.97   2  12    10 0.32    -0.92
## post.test.2    3 22  5.55 2.04    5.0    5.39 1.48   3  10     7 0.60    -0.88
## post.test.3    4 22 41.05 5.64   41.0   40.89 5.93  32  54    22 0.16    -0.55
##               se
## group*      0.00
## post.test.1 0.59
## post.test.2 0.44
## post.test.3 1.20
## ------------------------------------------------------------ 
## group: DRTA
##             vars  n  mean   sd median trimmed  mad min max range  skew kurtosis
## group*         1 22  2.00 0.00    2.0    2.00 0.00   2   2     0   NaN      NaN
## post.test.1    2 22  9.77 2.72   10.0    9.83 2.97   5  14     9 -0.11    -1.19
## post.test.2    3 22  6.23 2.09    6.0    6.33 1.48   0  11    11 -0.68     2.26
## post.test.3    4 22 46.73 7.39   48.5   47.50 7.41  30  57    27 -0.78    -0.27
##               se
## group*      0.00
## post.test.1 0.58
## post.test.2 0.45
## post.test.3 1.58
## ------------------------------------------------------------ 
## group: Strat
##             vars  n  mean   sd median trimmed  mad min max range  skew kurtosis
## group*         1 22  3.00 0.00      3    3.00 0.00   3   3     0   NaN      NaN
## post.test.1    2 22  7.77 3.93      7    7.67 4.45   1  15    14  0.23    -1.20
## post.test.2    3 22  8.36 2.90      9    8.56 2.97   1  13    12 -0.61    -0.11
## post.test.3    4 22 44.27 5.77     45   44.67 5.19  33  53    20 -0.62    -0.69
##               se
## group*      0.00
## post.test.1 0.84
## post.test.2 0.62
## post.test.3 1.23

The Basal group had an average score of 17.76. The DRTA group had an average score of 20.91. The Strat group had an average score of 20.13. These means clearly show a difference in Basal from the other teaching methods.

The boxplot again shows how the results of Basal differing from those of the other teaching methods. The means of Basal in every post.test are lower than those of the other two testing results.