{"id":3950,"date":"2025-12-05T13:13:42","date_gmt":"2025-12-05T13:13:42","guid":{"rendered":"https:\/\/www.chanakya-research.com\/blog\/?p=3950"},"modified":"2025-12-05T13:39:57","modified_gmt":"2025-12-05T13:39:57","slug":"choosing-your-statistical-weapon-real-world-examples-for-doctoral-analysis","status":"publish","type":"post","link":"https:\/\/www.chanakya-research.com\/blog\/choosing-your-statistical-weapon-real-world-examples-for-doctoral-analysis\/","title":{"rendered":"Choosing Your Statistical Weapon: Real-World Examples for Doctoral Analysis"},"content":{"rendered":"<p>Selecting the right statistical tool can feel overwhelming. Let\u2019s ground the process with concrete examples using common secondary datasets which are commonly used in PhD research. The crux remains like this:\u00a0Your question dictates your tool, and your data\u2019s nature validates that choice.<\/p>\n<p>Example 1: Financial Data of Listed Companies (Last 20 Years)<\/p>\n<p>Research Question:\u00a0<i>&#8220;Do firms with higher ESG (Environmental, Social, Governance) scores exhibit lower volatility in their stock returns during market downturns compared to firms with lower ESG scores?&#8221;<\/i><\/p>\n<ul>\n<li>Step 1 \u2013 Map the Question:\u00a0You are\u00a0comparing groups\u00a0(High-ESG vs. Low-ESG firms) on an\u00a0outcome\u00a0(stock return volatility, likely measured by standard deviation). You&#8217;re also considering a condition (<i>during market downturns<\/i>). This hints at a moderating or conditioning variable.<\/li>\n<li>Step 2 \u2013 Audit the Data:\u00a0Your dependent variable (volatility) is\u00a0continuous. Your key independent variable (ESG Group) is\u00a0categorical\u00a0(you might create a median split or use terciles). You have a massive\u00a0panel dataset\u00a0(multiple companies over 20 years\u2014repeated measures).<\/li>\n<li>Step 3 \u2013 Match &amp; Check Assumptions:\n<ul>\n<li>A simple independent t-test comparing the\u00a0<i>average volatility<\/i>\u00a0of the two groups across all years would be wrong\u2014it ignores the time series and repeated company data, violating the independence assumption.<\/li>\n<li>The correct tool is likely a\u00a0Panel Data Regression (Fixed\/Random Effects Model). This controls for unobserved, time-invariant company characteristics (e.g., inherent industry risk). You could model volatility as a function of ESG group, market condition (downturn=1, normal=0), and their interaction term. A significant interaction would answer your question.<\/li>\n<li>Assumptions to check: Serial correlation (Durbin-Watson test), heteroskedasticity, and stationarity of your volatility measure.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Example 2: Gold or Oil Prices (20-Year Daily\/Weekly Time Series)<\/p>\n<p>Research Question:\u00a0<i>&#8220;What is the long-term trend and seasonality component in monthly gold prices, and can we reliably forecast short-term future prices?&#8221;<\/i><\/p>\n<ul>\n<li>Step 1 \u2013 Map the Question:\u00a0This is a classic\u00a0time series analysis\u00a0question involving decomposition (trend, seasonality) and prediction.<\/li>\n<li>Step 2 \u2013 Audit the Data:\u00a0You have a\u00a0univariate time series\u2014a single variable (price) measured at regular intervals over time. The data points are\u00a0not independent; today&#8217;s price is heavily influenced by yesterday&#8217;s.<\/li>\n<li>Step 3 \u2013 Match &amp; Check Assumptions:\n<ul>\n<li>Descriptive\/Exploratory:\u00a0Begin with visualizations (line plot) and\u00a0time series decomposition\u00a0(using additive or multiplicative models) to isolate trend, seasonal, and irregular components.<\/li>\n<li>Forecasting:\u00a0Standard regression fails due to autocorrelation. The go-to tools are\u00a0ARIMA (AutoRegressive Integrated Moving Average)\u00a0or\u00a0Exponential Smoothing (ETS)\u00a0models.<\/li>\n<li>Crucial Pre-Step:\u00a0You must first test for\u00a0stationarity\u00a0using the\u00a0Augmented Dickey-Fuller (ADF) test. Non-stationary data (with a strong trend) must be differenced. For gold, you might also model returns (percentage change) instead of raw prices to achieve stationarity. You\u2019d then fit ARIMA models, diagnose residuals, and compare forecast accuracy (e.g., using Mean Absolute Percentage Error).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Example 3: USD\/INR Exchange Rate Fluctuations<\/p>\n<p>Research Question 1:\u00a0<i>&#8220;Is there a causal relationship between changes in the US Federal Reserve interest rate and the volatility of the USD\/INR exchange rate?&#8221;<\/i><\/p>\n<ul>\n<li>Step 1 \u2013 Map the Question:\u00a0You are examining a\u00a0dynamic relationship between two time series\u00a0and specifically asking about\u00a0causality and volatility.<\/li>\n<li>Step 2 \u2013 Audit the Data:\u00a0Two continuous time series: Fed rate (likely monthly) and a measure of INR volatility (e.g., the standard deviation of daily returns within that month).<\/li>\n<li>Step 3 \u2013 Match &amp; Check Assumptions:\n<ul>\n<li>Granger Causality Test:\u00a0Specifically designed to test if past values of one time series (Fed rate) help predict another (INR volatility). A significant result suggests &#8220;Granger-causality,&#8221; not true causality, but predictive power in a time-series context.<\/li>\n<li>Pre-requisite:\u00a0Both series must be\u00a0stationary. You would use the ADF test and difference the series if needed.<\/li>\n<li>Advanced Alternative:\u00a0To model volatility directly, you could use a\u00a0GARCH (Generalized Autoregressive Conditional Heteroskedasticity)\u00a0model. This is the standard tool in econometrics for modeling financial volatility clustering (periods of high volatility followed by high volatility).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Research Question 2:\u00a0<i>&#8220;Does the USD\/INR return series follow a normal distribution?&#8221;<\/i><\/p>\n<ul>\n<li>This is a foundational question about the\u00a0distribution\u00a0of your data.<\/li>\n<li>Tool:\u00a0Here, you are not modelling relationships. You are testing a property. Use\u00a0descriptive statistics\u00a0(skewness, kurtosis), a\u00a0Q-Q plot, and a formal test like the\u00a0Kolmogorov-Smirnov\u00a0or\u00a0Jarque-Bera test. The finding (it almost certainly will not be normal) will then inform your choice of other tools, pushing you towards non-parametric methods or distributions used in financial mathematics (like the Student&#8217;s t-distribution).<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Selecting the right statistical tool can feel overwhelming. Let\u2019s ground the process with concrete examples using common secondary datasets which are commonly used in PhD research. The crux remains like&#8230; <a href=\"https:\/\/www.chanakya-research.com\/blog\/choosing-your-statistical-weapon-real-world-examples-for-doctoral-analysis\/\">Read more &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47],"tags":[],"class_list":["post-3950","post","type-post","status-publish","format-standard","hentry","category-statistics-analysis"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/posts\/3950","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/comments?post=3950"}],"version-history":[{"count":1,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/posts\/3950\/revisions"}],"predecessor-version":[{"id":3951,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/posts\/3950\/revisions\/3951"}],"wp:attachment":[{"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/media?parent=3950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/categories?post=3950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.chanakya-research.com\/blog\/wp-json\/wp\/v2\/tags?post=3950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}