Thank you very much

It will be to process the data, because the analysis and interpretation is done by you.

You must use Simple Linear Regression

If you’re primary goal is to establish relationship between two variables you can use pearson r correlation (if your data is normally distributed), or spearman signed rand correlation (if data is not normally distributed). However, correlation here does not mean causation.

If you want go explore further and and “predict” if one variable is the reason the other one is increasing or decreasing then use simple regression.

Correlation Analysis: This will help you understand the strength and direction of the linear relationship between two variables (in this case, internal and external examination scores). You can calculate the Pearson correlation coefficient, which ranges from -1 to +1. A positive value indicates a positive correlation (as one variable increases, the other tends to increase), while a negative value indicates a negative correlation (as one variable increases, the other tends to decrease).

Regression Analysis: If you want to delve deeper into the relationship and potentially predict external examination scores based on internal examination scores, you can use regression analysis. Specifically, a simple linear regression would be appropriate here. In this analysis, the internal examination scores would be the independent variable (predictor), and the external examination scores would be the dependent variable (outcome). The regression model will help you quantify the relationship between these variables and allow you to make predictions. Ensure that your data meets the assumptions of the analysis you're planning to perform. For correlation and regression, assumptions include linearity, normality, homoscedasticity (constant variance), and independence. Remember that while you're looking for a relationship, this analysis won't establish causation. Higher internal examination scores might correlate with higher external scores, but other factors could be influencing the relationship as well.

There could be other factors that influence external examination scores, such as study habits, socioeconomic status, and teacher quality. If possible, collect additional data on these variables to perform a more comprehensive analysis. You will need statistical software to perform these analyses. Common options include R or Jamovi (open statistical software (https://www.jamovi.org/) and specialized statistical software like SPSS.

It is very confusing what you want to do. What you argue before the question you will find in the analysis you do of your resulting statistics. I recommend that you identify the problem you intend to study well, then ask yourself if you can solve it or not. Your answer to the question determines the type and design of your inquiry.

* Pearson r correlation can be used with exam scores. Don't use Spearman S here.

* Two-sample independent t-test

* Since you already mentioned that the two variables are dependent, I don't recommend you use regression.

You did not mention the number(s) of independent variable(s) but you can use Pearson r Correlation to test the relationship.

For data analysis to compare the two variables I used the t-student test for small samples to test the hypothesis of both groups. In the case of exam scores per question it is a single answer, therefore you could do, you could graph both groups in a single graph depending on the number of questions using Excel, or the GeoGebra program.

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When you're conducting a study to ascertain the relationship between two dependent variables, such as exam scores, you're essentially looking to analyze the correlation between these variables. To do this, you can use statistical tools and techniques designed for analyzing relationships and associations between variables. Two common methods you can consider are:

Pearson Correlation Coefficient:

The Pearson correlation coefficient, often denoted as "r," is a widely used statistical measure that quantifies the strength and direction of a linear relationship between two continuous variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no linear correlation.

To use the Pearson correlation coefficient:

Collect pairs of data points for the two dependent variables (e.g., exam scores for two different subjects).

Calculate the Pearson correlation coefficient using statistical software (such as Excel, SPSS, R, or Python libraries like NumPy and SciPy).

Interpret the coefficient to determine the strength and direction of the relationship.

Keep in mind that the Pearson correlation coefficient specifically measures linear relationships. If the relationship is nonlinear, other methods may be more appropriate.

Spearman Rank Correlation:

The Spearman rank correlation coefficient, denoted as "ρ" or "rs," assesses the strength and direction of a monotonic (nonlinear) relationship between two variables. It's particularly useful when the relationship is not strictly linear but still shows a consistent trend.

To use the Spearman rank correlation:

Rank the data for both dependent variables.

Calculate the Spearman rank correlation coefficient using statistical software.

Interpret the coefficient to understand the nature and strength of the relationship.

Choosing between Pearson and Spearman depends on the nature of the relationship you expect to find between the variables. If you're only interested in linear relationships, Pearson is appropriate. If you suspect a monotonic but not necessarily linear relationship, Spearman might be more suitable.

Both of these methods assume that the data points are independent and come from a continuous distribution. Before using any statistical analysis, ensure your data meets the assumptions of the chosen method. Additionally, always consider the context of your study and interpret the results in light of your research question.

If two variables are continuous then I think you must go fro Pearson ‘r’ to ascertain the correlation

Pearson's correlation coefficient (often denoted as 'r') is commonly used to measure the linear relationship between two continuous variables. It helps determine the strength and direction of the correlation. However, keep in mind that Pearson's 'r' is suitable only for linear relationships; if the relationship is nonlinear, other correlation measures like Spearman's rank correlation might be more appropriate.