Primary Phase: Individual Schools Budget vs Pupil Numbers

Linear Regression Analysis

# A tibble: 2 x 9
  Phase        data model term  estimate std.error statistic  p.value p.adjusted
  <fct> <list<df[,> <lis> <chr>    <dbl>     <dbl>     <dbl>    <dbl>      <dbl>
1 Prim~ [1,265 x 6] <lm>  (Int~    82.9     6.04        13.7 4.34e-40   3.47e-39
2 Prim~ [1,265 x 6] <lm>  `Pup~     3.20    0.0247     130.  0.         0.      

The regression shows that for the primary phase in Welsh schools, each individual student increases the Individual Schools Budget by £3,200. The p value returns a strong statistical significance (p adjusted = 0). Essentially, in 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is extremely low, at a value of 0.0247. This means that on average, the model will be incorrect by £24 plus or minus the median value.

Note that the nursery phase returned a non-significant p value and therefore was not analysed. This is likely due to the small number of nursery schools within Wales.

Interactive Data Table

Secondary Phase: Individual Schools Budget vs Pupil Numbers

Linear Regression Analysis

# A tibble: 2 x 9
  Phase       data model term  estimate std.error statistic   p.value p.adjusted
  <fct>  <list<df> <lis> <chr>    <dbl>     <dbl>     <dbl>     <dbl>      <dbl>
1 Secon~ [199 x 6] <lm>  (Int~   434.     66.2         6.57 4.51e- 10  2.25e-  9
2 Secon~ [199 x 6] <lm>  `Pup~     4.15    0.0701     59.3  1.53e-127  1.38e-126

The regression shows that for the secondary phase in Welsh schools, each individual student increases the Individual Schools Budget by £4,150. The p value returns a strong statistical significance (p adjusted = 1.38e-126). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is extremely low for this phase, at a value of 0.0701. This means that on average, the model will be incorrect by £70 plus or minus the median value.

Interactive Data Table

Middle Phase: Individual Schools Budget vs Pupil Numbers

Linear Regression Analysis

# A tibble: 2 x 9
  Phase       data model term   estimate std.error statistic  p.value p.adjusted
  <fct>  <list<df> <lis> <chr>     <dbl>     <dbl>     <dbl>    <dbl>      <dbl>
1 Middle  [19 x 6] <lm>  (Inte~   168.     196.        0.855 4.04e- 1   6.01e- 1
2 Middle  [19 x 6] <lm>  `Pupi~     4.39     0.224    19.6   4.22e-13   2.53e-12

The regression shows that for the middle phase in Welsh schools, each individual student increases the Individual Schools Budget by £4,390. The p value returns a strong statistical significance (p adjusted = 2.53e-12). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is very low, at a value of 0.24. This means that on average, the model will be incorrect by £224 plus or minus the median value.

Interactive Data Table

Special Phase: Individual Schools Budget vs Pupil Numbers

Linear Regression Analysis

# A tibble: 2 x 9
  Phase       data model term   estimate std.error statistic  p.value p.adjusted
  <fct>  <list<df> <lis> <chr>     <dbl>     <dbl>     <dbl>    <dbl>      <dbl>
1 Speci~  [41 x 6] <lm>  (Inte~    228.     218.        1.05 3.01e- 1   6.01e- 1
2 Speci~  [41 x 6] <lm>  `Pupi~     18.3      1.63     11.2  9.48e-14   6.63e-13

The regression shows that for the special phase in Welsh schools, each individual student increases the Individual Schools Budget by £18,300. The p value returns a strong statistical significance (p adjusted = 6.63e-13). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers.

However, the standard error is relatively larger than the other phases in this report, at a value of 1.63. This means that on average, the model will be incorrect by £1,630 plus or minus the median value. This increase in standard error is symptomatic of having a relatively small sample size in relation to the correlation coefficient and therefore would advise caution in drawing conclusions from this dataset.

Interactive Data Table