The answers depends on many factors. First, what is your measurement. Secondly, what size sample. Thirdly, and based upon 1 and 2, what statistical test. For example, an independent t test will require a much different sample size than confirmatory factor analysis.
Another key point: Differentiate statistical significance versus practical significance. For example, statistical significance is a factor partly based on sample size.
I believe that designing a quasi-experimental study would be a preferable approach. One group would receive intervention-based instruction, while the other group would undergo traditional teaching.
Statistical analysis would involve using an independent t-test.
To determine if there's a significant relationship between curriculum enhancements and learning growth rate, you can use various statistical tools depending on the nature of your data and your research design. Here are some popular options:
Correlation Analysis:If both curriculum enhancements and learning growth rate are measured on a continuous scale, you can use Pearson's correlation coefficient (r) to measure the strength and direction of the linear relationship between the two variables. For ordinal data, use Spearman's rank-order correlation.
T-test or ANOVA (Analysis of Variance):If you have a control group (using the old curriculum) and an experimental group (using the enhanced curriculum), and you want to compare the mean learning growth rate between these two groups, use a t-test. If you have multiple experimental groups (e.g., different types of curriculum enhancements), use ANOVA.
Regression Analysis:If you want to predict the learning growth rate based on the level of curriculum enhancement (especially if you have other control variables), use regression analysis. Multiple regression can be used if there are multiple predictor variables.
Chi-square Test:If both curriculum enhancements and learning growth rate are categorical (e.g., enhanced vs. not enhanced, high growth vs. low growth), use the Chi-square test for independence to determine if there's a significant relationship between the two.
Pre-Post Test Analysis:If you measure learning growth rate before and after introducing the curriculum enhancement for the same group, you can use a paired t-test. If you have multiple groups, a repeated measures ANOVA might be appropriate.
General Linear Models (GLM) or Generalized Linear Models:For more complex designs where you might want to account for both fixed and random effects or other types of distributions, you can use GLMs or Generalized Linear Models.
Non-parametric Tests:If your data does not meet the assumptions of parametric tests (e.g., normal distribution, homogeneity of variance), consider non-parametric alternatives such as the Mann-Whitney U test, Kruskal-Wallis test, or the Wilcoxon signed-rank test.
When selecting a statistical tool, consider the following:
The level of measurement of your data (nominal, ordinal, interval, ratio).
The distribution of your data (normal vs. non-normal).
The design of your study (paired vs. independent samples).
The number of groups or conditions you're comparing.
Remember to also check the assumptions of each statistical test and ensure that your data meets these assumptions before conducting the analysis. If the assumptions are not met, consider using an alternative test or transformation methods.
Before thinking about the statistical method to use, the question to ask is how are you going to measure those variables? Do you have the tool to measure it? If yes, then you can proceed from there.
Pearson is used for correlational analysis. If it is effect, then regression. However, I believe the gold standard now is PLS- SEM which already includes the correlation and regression. Just be mindful of the number of respondents for the result to be generalizable. Minimum is 250 or thereabouts.