2. Is there a significant difference on the variables grammatical aspect, technical aspect, and formal discussion and communication when grouped according to:

2.1 Sex


Call:
lm(formula = `Formal Discussion and Communication` ~ `Grammatical Aspect` + 
    `Technical Aspect`, data = Data)

Coefficients:
         (Intercept)  `Grammatical Aspect`    `Technical Aspect`  
              1.4195                0.2156                0.2939

From this, we may deduce that the data fail to satisfy two assumptions – Linearity and Homogeneity of Variance.

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2.1.1 Sex and Grammatical Aspect

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Grammatical Aspect`
W = 0.93797, p-value = 0.0001452

Since p-value = 0.0001452 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  1  2.2485  0.137
      98

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.


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# A tibble: 2 × 11
  Sex    variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Male   Grammatical Asp…    27   2.2   3.6      3   0.5  3.07 0.368 0.071 0.146
2 Female Grammatical Asp…    73   2     3.8      3   0.4  3.04 0.279 0.033 0.065

The mean of male and female is 3.067 and 3.044, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                    n statistic    df     p method        
* <chr>              <int>     <dbl> <int> <dbl> <chr>         
1 Grammatical Aspect   100     0.386     1 0.534 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

2.1.2 Sex and Technical Aspect

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Technical Aspect`
W = 0.90369, p-value = 2.116e-06

Since p-value = 2.116e-06 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  1  0.1361  0.713
      98

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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# A tibble: 2 × 11
  Sex    variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Male   Technical Aspect    27   1.6   3.6      3   0.5  2.90 0.401 0.077 0.159
2 Female Technical Aspect    73   1.6   3.6      3   0.4  2.92 0.377 0.044 0.088

The mean of male and female is 2.896 and 2.923, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                  n statistic    df     p method        
* <chr>            <int>     <dbl> <int> <dbl> <chr>         
1 Technical Aspect   100    0.0984     1 0.754 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

2.1.3 Sex and Formal Discussion and Communication

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Formal Discussion and Communication`
W = 0.95727, p-value = 0.002581

Since p-value = 0.002581 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  1  0.9437 0.3337
      98

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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# A tibble: 2 × 11
  Sex    variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Male   Formal Discussi…    27   2.4   3.8    3     0.4  2.93 0.338 0.065 0.134
2 Female Formal Discussi…    73   1.6   3.8    2.8   0.4  2.94 0.405 0.047 0.095

The mean of male and female is 2.926 and 2.937, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                                     n statistic    df     p method        
* <chr>                               <int>     <dbl> <int> <dbl> <chr>         
1 Formal Discussion and Communication   100    0.0471     1 0.828 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

2.2 Strand

2.2.1 Strand and Grammatical Aspect

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Grammatical Aspect`
W = 0.93797, p-value = 0.0001452

Since p-value = 0.0001452 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  3  0.9776 0.4067
      96

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
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# A tibble: 4 × 11
  Strand variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 GAS    Grammatical Asp…    20   2.2   3.6    3.1   0.6  3.06 0.35  0.078 0.164
2 HUMSS  Grammatical Asp…    35   2     3.6    3     0.4  2.99 0.334 0.057 0.115
3 ABM    Grammatical Asp…    18   2.6   3.8    3.1   0.4  3.16 0.279 0.066 0.139
4 STEM   Grammatical Asp…    27   2.6   3.6    3     0.4  3.04 0.231 0.044 0.091

The mean of GAS, HUMSS, ABM and STEM is 3.060, 2.994, 3.156, and 3.044, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                    n statistic    df     p method        
* <chr>              <int>     <dbl> <int> <dbl> <chr>         
1 Grammatical Aspect   100      3.15     3 0.369 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

2.2.2 Strand and Technical Aspect

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Technical Aspect`
W = 0.90369, p-value = 2.116e-06

Since p-value = 2.116e-06 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  3  2.0142 0.1171
      96

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
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# A tibble: 4 × 11
  Strand variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 GAS    Technical Aspect    20   2.6   3.4    3     0.2  2.96 0.201 0.045 0.094
2 HUMSS  Technical Aspect    35   1.6   3.6    3     0.5  2.90 0.443 0.075 0.152
3 ABM    Technical Aspect    18   2.2   3.6    3.1   0.2  3.07 0.35  0.082 0.174
4 STEM   Technical Aspect    27   1.6   3.6    2.8   0.4  2.81 0.398 0.077 0.157

The mean of GAS, HUMSS, ABM and STEM is 2.960, 2.897, 3.067, and 2.807, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                  n statistic    df      p method        
* <chr>            <int>     <dbl> <int>  <dbl> <chr>         
1 Technical Aspect   100      7.00     3 0.0717 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

2.2.3 Strand and Formal Discussion and Communication

Normality Test


    Shapiro-Wilk normality test

data:  Data$`Formal Discussion and Communication`
W = 0.95727, p-value = 0.002581

Since p-value = 0.002581 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  3     0.2 0.8962
      96

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameter

Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
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Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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# A tibble: 4 × 11
  Strand variable             n   min   max median   iqr  mean    sd    se    ci
  <fct>  <fct>            <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 GAS    Formal Discussi…    20   2.4   3.8    2.8  0.45  2.99 0.375 0.084 0.176
2 HUMSS  Formal Discussi…    35   2     3.8    3    0.3   2.94 0.378 0.064 0.13 
3 ABM    Formal Discussi…    18   1.6   3.8    2.8  0.4   2.84 0.488 0.115 0.243
4 STEM   Formal Discussi…    27   2.4   3.6    3    0.5   2.94 0.341 0.066 0.135

The mean of GAS, HUMSS, ABM and STEM is 2.990, 2.943, 2.844, and 2.941, respectively.

Mann Whitney U Test

# A tibble: 1 × 6
  .y.                                     n statistic    df     p method        
* <chr>                               <int>     <dbl> <int> <dbl> <chr>         
1 Formal Discussion and Communication   100     0.921     3  0.82 Kruskal-Wallis

Based on the p-value, there is no significant difference was observed between the group pairs.

3. Is there a significant difference between the variables grammatical aspect, technical aspect, and formal discussion and communication?

Normality Test


    Shapiro-Wilk normality test

data:  Data1$Scores
W = 0.94238, p-value = 1.973e-09

Since p-value = 1.973e-09 < 0.05, it is conclusive that we reject the null hypothesis. That is, we cannot assume normality.

Equality of Variance

Warning in leveneTest.default(y = y, group = group, ...): group coerced to
factor.

Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)
group   2  2.2677 0.1053
      297

The p-value is greater than the 0.05 level of significance. Thus, the homogeneity assumption of the variance is met.

Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
graphical parameter

Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" is not
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Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" is not a
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# A tibble: 3 × 11
  Variables      variable     n   min   max median   iqr  mean    sd    se    ci
  <fct>          <fct>    <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Grammatical A… Scores     100   2     3.8      3  0.4   3.05 0.304 0.03  0.06 
2 Technical Asp… Scores     100   1.6   3.6      3  0.4   2.92 0.382 0.038 0.076
3 Formal Discus… Scores     100   1.6   3.8      3  0.45  2.93 0.387 0.039 0.077

The mean of grammatical aspect, technical aspect, and formal discussion and communication is 3.050, 2.916, and 2.934, respectively.

Kruskal-wallis Test

# A tibble: 1 × 6
  .y.        n statistic    df       p method        
* <chr>  <int>     <dbl> <int>   <dbl> <chr>         
1 Scores   300      9.56     2 0.00839 Kruskal-Wallis

Based on the p-value, there is significant difference was observed between the group pairs.

Pairwise Comparisons

# A tibble: 3 × 9
  .y.    group1         group2    n1    n2 statistic       p  p.adj p.adj.signif
* <chr>  <chr>          <chr>  <int> <int>     <dbl>   <dbl>  <dbl> <chr>       
1 Scores Grammatical A… Techn…   100   100    -2.53  0.0113  0.0338 *           
2 Scores Grammatical A… Forma…   100   100    -2.80  0.00509 0.0153 *           
3 Scores Technical Asp… Forma…   100   100    -0.267 0.790   1      ns

There is significant difference between grammatical aspect and technical aspect so with grammatical aspect and formal discussion and communication.

4. On which variable have the most significant impact?

Based on the provided output above, we can say that it is the grammatical aspect.

ALTEA GRIAR GROUP STATISTICAL ANALYSIS

Kyle Kenneth Ruaya

2024-02-24

Data

1. What is the demographic profile of the respondents in terms of:

Sex

Strand

2. Is there a significant difference on the variables grammatical aspect, technical aspect, and formal discussion and communication when grouped according to:

2.1 Sex

2.1.1 Sex and Grammatical Aspect

Normality Test

Equality of Variance

Mann Whitney U Test

2.1.2 Sex and Technical Aspect

Normality Test

Equality of Variance

Mann Whitney U Test

2.1.3 Sex and Formal Discussion and Communication

Normality Test

Equality of Variance

Mann Whitney U Test

2.2 Strand

2.2.1 Strand and Grammatical Aspect

Normality Test

Equality of Variance

Mann Whitney U Test

2.2.2 Strand and Technical Aspect

Normality Test

Equality of Variance

Mann Whitney U Test

2.2.3 Strand and Formal Discussion and Communication

Normality Test

Equality of Variance

Mann Whitney U Test

3. Is there a significant difference between the variables grammatical aspect, technical aspect, and formal discussion and communication?

Normality Test

Equality of Variance

Kruskal-wallis Test

Pairwise Comparisons

4. On which variable have the most significant impact?