ANOVA
2022-12-07
Please help me check if I link the data correctly
## ID Executive.Networks D.prime C.score Anxiety Anxiety_level Stress
## 1 SADP01 149.55 1.100000 1.65000 14 Moderate 18
## 2 SADP05 187.46 2.040000 2.09000 25 Extreme 26
## 3 SADP09 125.05 0.820000 1.56000 28 Extreme 41
## 4 SADP11 124.16 1.880000 2.04000 16 Severe 27
## 5 SADP13 182.02 0.800000 1.52000 38 Extreme 47
## 6 SADP14 218.83 0.900000 1.61000 28 Extreme 26
## 7 SADP15 152.98 0.480000 1.36000 15 Severe 14
## 8 SADP18 179.28 0.540000 1.31000 14 Moderate 20
## 9 SADP25 116.82 1.200000 1.73000 18 Severe 27
## 10 SADP27 216.76 0.960000 1.58000 44 Extreme 42
## 11 SADP29 287.74 0.690000 1.41000 28 Extreme 31
## 12 SADP30 170.71 0.670000 1.38000 16 Severe 15
## 13 SADP36 78.94 2.210000 2.14000 19 Severe 21
## 14 SADP37 216.64 2.110000 2.11000 18 Severe 22
## 15 SADP40 78.42 0.940000 1.51000 14 Moderate 14
## 16 SADP42 160.49 2.180000 2.16000 25 Extreme 29
## 17 SADP43 136.10 1.273850 1.69335 16 Severe 16
## 18 SADP44 363.52 0.698350 1.51810 46 Extreme 51
## 19 SADP45 242.28 0.720700 1.46275 34 Extreme 45
## 20 SADP46 88.30 -0.098850 1.15480 15 Severe 18
## 21 SADP47 146.93 0.775450 1.42725 7 Normal 11
## 22 SADP49 266.71 1.098300 1.58870 28 Extreme 17
## 23 SADP50 102.96 0.000000 1.45855 24 Extreme 22
## 24 SADP51 150.27 0.668250 1.45135 22 Extreme 26
## 25 SADP52 156.36 0.376500 1.56560 35 Extreme 37
## 26 SADP53 235.12 1.175800 1.61250 21 Extreme 24
## 27 SADP54 -38.92 -0.225000 1.10810 6 Normal 5
## 28 SADP55 298.51 1.045150 1.50410 29 Extreme 28
## 29 SADP56 -10.14 0.868800 1.41465 15 Severe 12
## 30 SADP57 174.66 0.553400 1.42770 9 Mild 14
## 31 SADP58 224.30 0.922650 1.54665 9 Mild 6
## 32 SADP59 183.41 0.970050 1.48100 20 Extreme 19
## 33 SADP60 143.33 0.911300 1.54150 13 Moderate 10
## 34 SADP61 204.91 1.192750 1.73390 8 Mild 11
## 35 SADP62 227.43 0.491950 1.34725 11 Moderate 8
## 36 SADP63 281.91 1.275300 1.69265 8 Mild 23
## 37 SADP65 189.78 NA NA 7 Normal 5
## 38 SADP66 158.42 0.710000 1.45980 5 Normal 3
## 39 SADP67 108.24 1.238350 1.62930 12 Moderate 14
## 40 SADP68 16.19 0.955750 1.54880 10 Moderate 8
## 41 SADP69 201.20 0.714700 1.50765 9 Mild 5
## 42 SADP70 206.99 0.565000 1.50395 17 Severe 23
## 43 SADP71 240.47 0.874450 1.49220 4 Normal 10
## 44 SADP72 218.00 2.082650 2.06590 25 Extreme 26
## 45 SADP73 114.94 1.002500 1.55620 4 Normal 21
## 46 SADP74 266.21 0.755505 1.46285 1 Normal 9
## 47 SADP75 101.80 0.970050 1.48100 12 Moderate 8
## 48 SADP76 193.02 0.565000 1.50395 18 Severe 28
## 49 SADP77 64.52 0.557000 1.39630 29 Extreme 29
## 50 SADP78 193.88 0.911100 1.51050 10 Moderate 17
## 51 SADP80 35.83 1.045150 1.50410 6 Normal 10
## 52 SADP81 205.33 0.077700 1.41620 1 Normal 4
## 53 SADP82 130.55 1.129500 1.63565 20 Extreme 23
## 54 SADP83 293.04 0.874450 1.49220 17 Severe 20
## 55 SADP85 160.77 0.557000 1.39630 25 Extreme 18
## Stress_level Depression Depression_level
## 1 Mild 18 Moderate
## 2 Severe 23 Severe
## 3 Extreme 31 Extreme
## 4 Severe 22 Severe
## 5 Extreme 40 Extreme
## 6 Severe 20 Moderate
## 7 Normal 14 Moderate
## 8 Moderate 14 Moderate
## 9 Severe 42 Extreme
## 10 Extreme 48 Extreme
## 11 Severe 25 Severe
## 12 Mild 19 Moderate
## 13 Moderate 15 Moderate
## 14 Moderate 18 Moderate
## 15 Normal 14 Moderate
## 16 Severe 34 Extreme
## 17 Mild 14 Moderate
## 18 Extreme 23 Severe
## 19 Extreme 33 Extreme
## 20 Mild 11 Mild
## 21 Normal 9 Normal
## 22 Mild 18 Moderate
## 23 Moderate 17 Moderate
## 24 Severe 17 Moderate
## 25 Extreme 37 Extreme
## 26 Moderate 16 Moderate
## 27 Normal 8 Normal
## 28 Severe 34 Extreme
## 29 Normal 10 Mild
## 30 Normal 17 Moderate
## 31 Normal 8 Normal
## 32 Moderate 17 Moderate
## 33 Normal 8 Normal
## 34 Normal 17 Moderate
## 35 Normal 0 Normal
## 36 Moderate 16 Moderate
## 37 Normal 2 Normal
## 38 Normal 4 Normal
## 39 Normal 7 Normal
## 40 Normal 4 Normal
## 41 Normal 1 Normal
## 42 Moderate 13 Mild
## 43 Normal 1 Normal
## 44 Severe 28 Extreme
## 45 Moderate 8 Normal
## 46 Normal 2 Normal
## 47 Normal 16 Moderate
## 48 Severe 13 Mild
## 49 Severe 10 Mild
## 50 Mild 3 Normal
## 51 Normal 5 Normal
## 52 Normal 3 Normal
## 53 Moderate 18 Moderate
## 54 Moderate 16 Moderate
## 55 Mild 22 SevereExecutive Networks — NOT SIGNIFICANT
We target:
1. Is there a main effect of Anxiety level (Normal, Mild, Moderate,
Severe, Extreme) on Executive Network?
2. Is there a main effect of Depression level (Normal, Mild, Moderate,
Severe, Extreme) on Executive Network?
3. Is there a main effect of Stress level (Normal, Mild, Moderate,
Severe, Extreme) on Executive Network?
4. Is there an interaction effect between Anxiety and
Depression level on Executive Network?
5. Is there an interaction effect between Anxiety and
Stress level on Executive Network?
6. Is there an interaction effect between Stress and
Depression level on Executive Network?
7. Is there an interaction effect between Anxiety, Stress, and
Depression level on Executive Network?
## Call:
## aov(formula = Executive.Networks ~ Stress_level * Anxiety_level *
## Depression_level, data = df)
##
## Terms:
## Stress_level Anxiety_level Depression_level
## Sum of Squares 32446.30 37668.63 22122.48
## Deg. of Freedom 4 4 4
## Stress_level:Anxiety_level Stress_level:Depression_level
## Sum of Squares 22416.69 36444.12
## Deg. of Freedom 6 6
## Anxiety_level:Depression_level Residuals
## Sum of Squares 21272.96 159200.57
## Deg. of Freedom 3 27
##
## Residual standard error: 76.78748
## 97 out of 125 effects not estimable
## Estimated effects may be unbalanced## Df Sum Sq Mean Sq F value Pr(>F)
## Stress_level 4 32446 8112 1.376 0.269
## Anxiety_level 4 37669 9417 1.597 0.204
## Depression_level 4 22122 5531 0.938 0.457
## Stress_level:Anxiety_level 6 22417 3736 0.634 0.702
## Stress_level:Depression_level 6 36444 6074 1.030 0.428
## Anxiety_level:Depression_level 3 21273 7091 1.203 0.328
## Residuals 27 159201 5896D Prime — Only Depression has the main effect on D prime. No Interaction was found.
We target:
1. Is there a main effect of Anxiety level (Normal, Mild, Moderate,
Severe, Extreme) on D Prime?
2. Is there a main effect of Depression level (Normal, Mild, Moderate,
Severe, Extreme) on D Prime?
3. Is there a main effect of Stress level (Normal, Mild, Moderate,
Severe, Extreme) on D Prime?
4. Is there an interaction effect between Anxiety and
Depression level on D Prime?
5. Is there an interaction effect between Anxiety and
Stress level on D Prime?
6. Is there an interaction effect between Stress and
Depression level on D Prime?
7. Is there an interaction effect between Anxiety, Stress, and
Depression level on D Prime?
## Call:
## aov(formula = D.prime ~ Stress_level * Anxiety_level * Depression_level,
## data = df)
##
## Terms:
## Stress_level Anxiety_level Depression_level
## Sum of Squares 2.398726 0.481932 2.830890
## Deg. of Freedom 4 4 4
## Stress_level:Anxiety_level Stress_level:Depression_level
## Sum of Squares 1.159990 1.511599
## Deg. of Freedom 6 6
## Anxiety_level:Depression_level Residuals
## Sum of Squares 0.416591 5.926194
## Deg. of Freedom 3 26
##
## Residual standard error: 0.4774207
## 97 out of 125 effects not estimable
## Estimated effects may be unbalanced
## 1 observation deleted due to missingness## Df Sum Sq Mean Sq F value Pr(>F)
## Stress_level 4 2.399 0.5997 2.631 0.0572 .
## Anxiety_level 4 0.482 0.1205 0.529 0.7157
## Depression_level 4 2.831 0.7077 3.105 0.0325 *
## Stress_level:Anxiety_level 6 1.160 0.1933 0.848 0.5449
## Stress_level:Depression_level 6 1.512 0.2519 1.105 0.3860
## Anxiety_level:Depression_level 3 0.417 0.1389 0.609 0.6150
## Residuals 26 5.926 0.2279
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessBecause only Depression level has a main effect on D Prime, I would recommend performing one way ANOVA for Depression level on D Prime.
Target: Is there a significant different in D Prime in different Depression level? — - NOT SIGNIFICANT!
## Call:
## aov(formula = D.prime ~ Depression_level, data = df)
##
## Terms:
## Depression_level Residuals
## Sum of Squares 2.255743 12.470178
## Deg. of Freedom 4 49
##
## Residual standard error: 0.5044734
## Estimated effects may be unbalanced
## 1 observation deleted due to missingness## Df Sum Sq Mean Sq F value Pr(>F)
## Depression_level 4 2.256 0.5639 2.216 0.0809 .
## Residuals 49 12.470 0.2545
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessC Score — Only Depression and Stress has the main effect on C Score. No Interaction was found.
We target:
1. Is there a main effect of Anxiety level (Normal, Mild, Moderate,
Severe, Extreme) on C Score?
2. Is there a main effect of Depression level (Normal, Mild, Moderate,
Severe, Extreme) on C Score?
3. Is there a main effect of Stress level (Normal, Mild, Moderate,
Severe, Extreme) on C Score?
4. Is there an interaction effect between Anxiety and
Depression level on C Score?
5. Is there an interaction effect between Anxiety and
Stress level on C Score?
6. Is there an interaction effect between Stress and
Depression level on C Score?
7. Is there an interaction effect between Anxiety, Stress, and
Depression level on C Score?
## Call:
## aov(formula = C.score ~ Stress_level * Anxiety_level * Depression_level,
## data = df)
##
## Terms:
## Stress_level Anxiety_level Depression_level
## Sum of Squares 0.5597389 0.0957010 0.4767797
## Deg. of Freedom 4 4 4
## Stress_level:Anxiety_level Stress_level:Depression_level
## Sum of Squares 0.2494700 0.1703638
## Deg. of Freedom 6 6
## Anxiety_level:Depression_level Residuals
## Sum of Squares 0.0828002 1.0486322
## Deg. of Freedom 3 26
##
## Residual standard error: 0.2008283
## 97 out of 125 effects not estimable
## Estimated effects may be unbalanced
## 1 observation deleted due to missingness## Df Sum Sq Mean Sq F value Pr(>F)
## Stress_level 4 0.5597 0.13993 3.470 0.0212 *
## Anxiety_level 4 0.0957 0.02393 0.593 0.6706
## Depression_level 4 0.4768 0.11919 2.955 0.0388 *
## Stress_level:Anxiety_level 6 0.2495 0.04158 1.031 0.4279
## Stress_level:Depression_level 6 0.1704 0.02839 0.704 0.6491
## Anxiety_level:Depression_level 3 0.0828 0.02760 0.684 0.5697
## Residuals 26 1.0486 0.04033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessBecause Depression level has a main effect on C Score, I would recommend performing one way ANOVA for Depression level on C Score.
Target: Is there a significant different in C Score in different Depression level? —- – YAY!!!! SIGNIFICANT!
## Call:
## aov(formula = C.score ~ Depression_level, data = df)
##
## Terms:
## Depression_level Residuals
## Sum of Squares 0.4970014 2.1864845
## Deg. of Freedom 4 49
##
## Residual standard error: 0.2112395
## Estimated effects may be unbalanced
## 1 observation deleted due to missingness## Df Sum Sq Mean Sq F value Pr(>F)
## Depression_level 4 0.497 0.12425 2.785 0.0366 *
## Residuals 49 2.187 0.04462
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessTukey Test – NOT SIGNIFICANT
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = C.score ~ Depression_level, data = df)
##
## $Depression_level
## diff lwr upr p adj
## Mild-Normal -0.07582667 -0.38474503 0.2330917 0.9566051
## Moderate-Normal 0.12037083 -0.08395946 0.3247011 0.4625418
## Severe-Normal 0.22032333 -0.08859503 0.5292417 0.2720430
## Extreme-Normal 0.21259333 -0.03963746 0.4648241 0.1361635
## Moderate-Mild 0.19619750 -0.10291142 0.4953064 0.3534822
## Severe-Mild 0.29615000 -0.08219619 0.6744962 0.1907782
## Extreme-Mild 0.28842000 -0.04524997 0.6220900 0.1198815
## Severe-Moderate 0.09995250 -0.19915642 0.3990614 0.8772307
## Extreme-Moderate 0.09222250 -0.14789406 0.3323391 0.8119874
## Extreme-Severe -0.00773000 -0.34139997 0.3259400 0.9999956
Scheffe Test - NOT SIGNIFICANT
##
## Posthoc multiple comparisons of means: Scheffe Test
## 95% family-wise confidence level
##
## $Depression_level
## diff lwr.ci upr.ci pval
## Mild-Normal -0.07582667 -0.42497086 0.2733175 0.9744
## Moderate-Normal 0.12037083 -0.11056635 0.3513080 0.5985
## Severe-Normal 0.22032333 -0.12882086 0.5694675 0.4064
## Extreme-Normal 0.21259333 -0.07248171 0.4976684 0.2399
## Moderate-Mild 0.19619750 -0.14185991 0.5342549 0.4930
## Severe-Mild 0.29615000 -0.13146256 0.7237626 0.3110
## Extreme-Mild 0.28842000 -0.08869883 0.6655388 0.2173
## Severe-Moderate 0.09995250 -0.23810491 0.4380099 0.9238
## Extreme-Moderate 0.09222250 -0.17916086 0.3636059 0.8793
## Extreme-Severe -0.00773000 -0.38484883 0.3693888 1.0000
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Bonferroni Method
##
## Pairwise comparisons using t tests with pooled SD
##
## data: df$C.score and df$Depression_level
##
## Normal Mild Moderate Severe
## Mild 1.00 - - -
## Moderate 1.00 0.69 - -
## Severe 0.49 0.31 1.00 -
## Extreme 0.21 0.18 1.00 1.00
##
## P value adjustment method: bonferroniBecause Stress level has a main effect on C Score, I would recommend performing one way ANOVA for Depression level on C Score.
Target: Is there a significant different in C Score in different Stress level? —- – YAY!!!! SIGNIFICANT!
## Call:
## aov(formula = C.score ~ Stress_level, data = df)
##
## Terms:
## Stress_level Residuals
## Sum of Squares 0.5597389 2.1237470
## Deg. of Freedom 4 49
##
## Residual standard error: 0.2081869
## Estimated effects may be unbalanced
## 1 observation deleted due to missingness## Df Sum Sq Mean Sq F value Pr(>F)
## Stress_level 4 0.5597 0.13993 3.229 0.0198 *
## Residuals 49 2.1237 0.04334
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 1 observation deleted due to missingnessDescriptive Statistics
## # A tibble: 5 × 4
## Stress_level N Mean SD
## <fct> <int> <dbl> <dbl>
## 1 Normal 20 1.47 0.126
## 2 Mild 7 1.48 0.187
## 3 Moderate 11 1.64 0.262
## 4 Severe 11 1.72 0.305
## 5 Extreme 6 1.53 0.0432Tukey Test - SIGNIFICANT between Severe and Normal
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = C.score ~ Stress_level, data = df)
##
## $Stress_level
## diff lwr upr p adj
## Mild-Normal 0.01253421 -0.24814020 0.2732086 0.9999197
## Moderate-Normal 0.16628421 -0.05708589 0.3896543 0.2331038
## Severe-Normal 0.25436603 0.03099593 0.4777361 0.0182274
## Extreme-Normal 0.06499254 -0.21110029 0.3410854 0.9626001
## Moderate-Mild 0.15375000 -0.13130485 0.4388049 0.5500640
## Severe-Mild 0.24183182 -0.04322303 0.5268867 0.1318347
## Extreme-Mild 0.05245833 -0.27554978 0.3804664 0.9910440
## Severe-Moderate 0.08808182 -0.16331293 0.3394766 0.8575618
## Extreme-Moderate -0.10129167 -0.40051127 0.1979279 0.8720991
## Extreme-Severe -0.18937348 -0.48859309 0.1098461 0.3896018
Boxplot
## Warning: Removed 1 rows containing non-finite values (`stat_boxplot()`).
A One Way ANOVA indicated that there is a significant difference in C score between different Stress Levels, F(4,49) = 3.229, p < 0.05. A post hoc Tukey test indicated that there is a significant difference in C score between Normal (M = 1.47, SD = 0.23) and Extreme level (M = 1.53, SD = 0.04). No other pair-wise difference found.