Selection of Statistical Test

The first research question deals with two quantitative values: volume and value. Since we are testing if there is no positive correlation between the two features and not just any relation, a one-tailed Pearson correlation test is the appropriate statistical method for the following reasons:

1. Both variables are continuous and measured on an interval/ratio scale
2. We are investigating a linear relationship between the variables
3. The hypothesis is directional (specifically testing for a positive correlation)

Statistical Analysis Results

The Pearson correlation coefficient (r) calculated between production volume and economic value is 0.4275, indicating a moderate positive linear relationship between the two variables. According to established statistical guidelines, correlation coefficients between 0.3 and 0.5 typically represent moderate positive correlations.

The one-tailed p-value is p is less than 0.0001, which is significantly below our alpha threshold of 0.05. This extremely small p-value indicates that the probability of observing this correlation coefficient (or stronger) by random chance alone, assuming the null hypothesis is true, is less than 0.01%. Therefore, we have sufficient statistical evidence to reject the null hypothesis.

Visual Analysis and Implications

To visually support this claim, we can utilize our plot from 3.2.7 but now we add a regression line.

The scatter plot reveals an interesting pattern that might not be fully captured by a single correlation coefficient. Upon visual inspection, there appear to be two distinct clusters within the data, suggesting a potentially more complex relationship. With this, we use K-means clustering to identify the two visually identifiable clustering.

The plot above is quite interesting as compared to what we could have imagined (most would easily halve the original scatter plot into two by creating a dividing line that will cluster the original scatter plot). But does these two plots inherit the same regression line from the original plot?

The first clustering has a high positive coefficient while the second clustering tends to have a lower negative coefficient. Given these two plots, it is hard to conclude what characteristics can be discerned from approximately 66% of production volume values. But after some point, economic value tends to die down.

This statistical result have economic implications. The positive correlation between production volume and economic value suggests that, in general, increasing aquaculture production leads to higher economic returns. However, the cluster analysis reveals a variation where:

• Cluster 0: A strong positive relationship exists (y = 7.905x + 56,991.36), suggesting efficient market conditions where increasing production significantly boosts economic value.
• Cluster 1: The relationship becomes negative (y = -2.059x + 3,893,432.51), indicating diminishing returns, likely due to market saturation or price suppression at high volumes.

These findings makes sense because it reflects the law of demand and supply. After some point, we cannot value the same good similar to the one previously bought due to decreasing marginal utility. Aside from that, there are income effects and demand shifts that needs to be considered especially that we are living in a third-world country and are currently facing high taxes. As a conclusion, where producers face market and policy constraints, this suggests that maximizing production may not always maximize profit.

Selection of Statistical Test

For this research question, we are dealing with a categorical variable as a predictor (region) and a quantitative outcome variable (production volume). Based on this, the appropriate statistical test for comparing more than two independent groups is the Kruskal-Wallis H test, a non-parametric alternative to one-way ANOVA when normality cannot be assumed.

Statistical Analysis Results

Using the ANOVA method (`f_oneway`), we obtained an F-statistic of 45 and a p-value of $3.25 \times 10^-35$. Given the extremely small p-value (far below any conventional alpha level), we reject the null hypothesis that all regional aquaculture volumes come from the same distribution.

This result indicates a statistically significant difference in aquaculture production volume across different regions in the Philippines. The variation is substantial enough to merit closer examination of regional contributions and disparities.

Visual Analysis and Implications

This tells us that every region has their own contribution and no conclusion can be said that could summarize the volume of aquaculture each region provides. This discrepancy allows us to identify weak points which we could prepare for or plan about. There might be some lack of support or some hidden cause that could lead to such discrepancy.

This can be further shown by the boxplots below, excluding outliers for each region. BARMM is quite an interesting case having a healthy production volume. If we geographically locate BARMM, it is located in the south-western part of the Philippines and is comprised of several islands and a mainland Mindanao area. Given its geographical location, we can already infer as to why BARMM produces such high highs in terms of volume.

If we think about it, several other regions especially in the Visayas are surrounded by large bodies of water but if we take a closer look, Western Visayas have greater proportions compared to Central and Eastern Visayas. Western Visayas has a well-established and well-supported aquaculture industry, backed by strong infrastructure and government investment. Key highlights include Capiz as the seafood capital, the Iloilo Fish Port Complex as a major trading and processing hub, a rehabilitated hatchery in Aklan producing up to 10 million bangus fry annually (operational since 2021), and plans for a ₱30 million aquaculture feed mill to lower feed costs. Central Visayas engages in aquaculture, particularly in Cebu and Siquijor, but faces economic and social challenges. A 2015 study found that while the sector offers employment, jobs are often non-permanent and poverty remains high in surrounding communities. Most farms use basic infrastructure like mud-bottom ponds and rely on commercial feed and free-flowing water systems, raising concerns about long-term sustainability. Eastern Visayas shows aquaculture potential, with feasibility studies supporting hatchery development. However, the region is highly vulnerable to typhoons, which threaten aquaculture operations and infrastructure.

Aside from the regions that are surrounded by bodies of water, there is also another interesting instance where Central Luzon, which is known for its vast lands for farming and agricultural products, is the second in terms of production volume. The study by Manlosa et al. (2021) explores how institutional dynamics and environmental changes have driven the expansion of aquaculture in Central Luzon, particularly highlighting the conversion of rice paddies into fish farms. A key driver of this shift is saltwater intrusion in low-lying areas, which made rice farming less viable and prompted farmers—especially in Pampanga, Bulacan, and Bataan—to transition to brackishwater aquaculture. These areas, along with inland provinces like Nueva Ecija and Tarlac, now contribute significantly to aquaculture production, cultivating species such as bangus, sugpo, and tilapia in fishponds, cages, and reservoirs.

Selection of Statistical Test

For analyzing the production volume trend over time, the Mann-Kendall Trend Test was selected as the appropriate statistical method. This test is ideal for this analysis because:

• It effectively detects monotonic trends in time series data
• It doesn't require the data to be normally distributed
• It can handle seasonal variations common in production data
• It's resistant to outliers which appear present in the quarterly production volumes

Statistical Analysis Results

Given that the trend is no trend, this means that there's no significant trend, thus we fail to reject `Ho`. This tells us about the uncertainty of the possible volume of aquaculture that we'll have for the following years. This uncertainty can cause several implications such as:

• Difficulty in long-term planning for supply chain management, including storage, distribution, and market pricing.
• Challenges in policy-making for the aquaculture sector, as the absence of a clear trend makes it harder to design effective interventions or subsidies.
• Risk for investors and stakeholders in the aquaculture industry who rely on production forecasts for business decisions.
• Potential instability in food security, especially if future volumes fluctuate unexpectedly, affecting local consumption and export goals

Visual Analysis and Implications

This can be further illustrated by the time series graph below which shows that there is indeed no apparent trend for the past five years.

From these plots, we get to learn that there are no apparent upward or downward patterns for quarterly fluctuations. There are some notable peaks that occurred in Q3 2022, Q4 2021, and Q3 2023, with the highest volume reaching nearly 6,000 metric tons. Q4 2021 and Q3 2022 are interesting cases because these are times where we're still under the Covid 19 pandemic.