# Statistical Analysis to Evaluate Education Endowment

Statistical analysis is the art of gathering data and revealing patterns and trends. After researchers have collected data, they can manipulate and analyze it to find key measures of location, calculate measures of spread, test a hypothesis, and predict the future based on the past behavior of data. Statistical analysis is extensively used in physics and social sciences to approximate values that are impossible or difficult to measure.

## Effects of Training on near-transfer and far-transfer in students with ADHD and/or RD

We use a 2 (experimental group and control group) x 4 (ADHD, RD, Comorbid, and TD) Mixed Model ANOVA with repeated measures on the near-transfer measures and far-transfer measures, i.e. for each pretest and posttest pairs for PQ_BRIEF, TQ_BRIEF, BackwardDigit and SWMBE – near transfer measures, and SWAN, TQ_SWAN and WordReading – far transfer measures. The Mixed Model ANOVA is used to test for mean differences between the two independent groups (Group and Intervention group) while subjecting participants to repeated measures (Pretests and Posttests).
1. NEAR-TRANSFER MEASURES
2. PQ_BRIEF
The results of the main effect due to the within-subjects, PQ_BRIEF (F=0.9, p-value = 0.344) indicate a lack of significant effects. This means there is no significant difference in the PQ_BRIEF measure before and after the training. The interaction between PQ_BRIEF and Intervention Group is also not significant (F=0.244, p-value = 0.637). This means there is no significant difference in the change of PQ_BRIEF between the experimental group and the control group.
The results of the test of the effect due to the between-subjects variable, Intervention_group is significant (F=56.027, p-value = 0.000). This means that the PQ_BRIEF values differ on the dependent variable, depending on their group i.e. between experimental and control groups.
The results of the main effect due to the within-subjects, TQ_BRIEF (F=0.222, p-value = 0.638) indicate a lack of significant effects. This means there is no significant difference in the TQ_BRIEF measure before and after the training. The interaction between TQ_BRIEF and Intervention Group is significant (F=8.629, p-value = 0.004). This means there is a significant difference in the change of TQ_BRIEF between the experimental group and the control group.

### Hypothesis Testing

The results of the test of the effect due to the between-subjects variable, Intervention_group is significant (F=56.755, p-value = 0.000). This means that the TQ_BRIEF values differ on the dependent variable, depending on their group i.e. between experimental and control groups.
The results of the main effect due to the within-subjects, SWMBE (F=10.773, p-value = 0.001) indicate a significant effect. This means there is a significant difference in SWMBE measure before and after the training. The interaction between SWMBE and Intervention Group is not significant (F=0.003, p-value = 0.954). This means there is no significant difference in the change of SWMBE between the experimental group and the control group.
The results of the test of the effect due to the between-subjects variable, Intervention_group is not significant (F=0.10, p-value = 0.922). This means that the SWMBE values do not differ on the dependent variable, depending on their group i.e. between experimental and control groups.
The results of the main effect due to the within-subjects, Backward Digit (F=2.458, p-value = 0.119) indicate a lack of a significant effect. This means there is no significant difference in the Backward Digit measure before and after the training. The interaction between Backward Digit and Intervention Group is also not significant (F=0. 563, p-value = 0.552). This means there is no significant difference in the change of the Backward Digit between the experimental group and the control group.
The results of the test of the effect due to the between-subjects variable, Intervention_group is significant (F=6.224, p-value = 0.014). This means that the Backward Digit values differ on the dependent variable, depending on their group i.e. between experimental and control groups.
The results of the main effect due to the within-subjects, PQ_SWAN (F=0.612, p-value = 0.435) indicate a lack of a significant effect. This means there is no significant difference in the PQ_SWAN measure before and after the training. The interaction between PQ_SWAN and Intervention Group is also not significant (F=0. 094, p-value = 0.760). This means there is no significant difference in the change of PQ_SWAN between the experimental group and the control group.
The results of the test of the effect due to the between-subjects variable, Intervention_group is significant (F=51.477, p-value = 0.000). This means that the PQ_SWAN values differ on the dependent variable, depending on their group i.e. between experimental and control groups.
The results of the main effect due to the within-subjects, TQ_SWAN (F=2.183, p-value = 0.142) indicate a lack of a significant effect. This means there is no significant difference in the TQ_SWAN measure before and after the training. The interaction between TQ_SWAN and Intervention Group is also not significant (F=2.698, p-value = 0.103). This means there is no significant difference in the change of TQ_SWAN between the experimental group and the control group.
The results of the main effect due to the within-subjects, Word Reading (F=57.46, p-value = 0.000) indicate a significant effect. This means there is a significant difference in Word Reading measure before and after the training. The interaction between Word Reading and Intervention Group is also not significant (F=0. 094, p-value = 0.760). This means there is no significant difference in the change of Word Reading between the experimental group and the control group. To get professional assistance with this area, take our hypothesis testing assignment help.

### Analysis of Variance

We use a 2 (experimental group and control group) x 4 (ADHD, RD, Comorbid, and TD) ANCOVA with Posttests as the dependent variable and control for pretests i.e. use pretests as covariates.
Analysis of Covariance (ANCOVA) is used to test the difference in the post-training measures among the training group while controlling for pretest measures. ANCOVA model will be modeled for each variable in the near-transfer measures and far-transfer measures, i.e. PQ_BRIEF, TQ_BRIEF, BackwardDigit, and SWMBE – near transfer measures, and SWAN, TQ_SWAN and WordReading – far transfer measures.
There was an overall statistically significant difference in post-training PQ_BRIEF among the different training groups once their means had been adjusted for pre-training measurements (F=4.209, p-value=0.007).
RD and TD groups reported a significant difference in post-training PQ_BRIEF once their means had been adjusted for pre-training measurements are, (p-value = 0.006).
There was an overall statistically significant difference in post-training TQ_BRIEF among the different training groups once their means had been adjusted for pre-training measurements (F=6.499, p-value=0.000). The groups that reported a significant difference in post-training TQ_BRIEF once their means had been adjusted for pre-training measurements are ADHD and TD (p-value = 0.015), RD, and TD (p-value=0.002), and Comorbid and TD (p-value = 0.001).
1. SWMBE There was a lack of overall statistically significant difference in post-training TQ_BRIEF among the different training groups once their means had been adjusted for pre-training measurements (F=0.464, p-value=0.708).
1. Backward Digit There was an overall statistically significant difference in post-training Backward Digit among the different training groups once their means had been adjusted for pre-training measurements (F=3.162, p-value=0.027). FAR-TRANSFER MEASURES
PQ_SWAN There was a lack of overall statistically significant difference in post-training PQ_SWAN among the different training groups once their means had been adjusted for pre-training measurements (F=1.280, p-value=0.284). There was a lack of overall statistically significant difference in post-training TQ_SWAN among the different training groups once their means had been adjusted for pre-training measurements (F=1.236, p-value=0.299). 