Quantitative Analysis Statistics Notes

Getting Your Data Ready Before You Run Any Numbers

The first thing most people mess up with quantitative analysis statistics notes is treating the formatting as an afterthought. You can't just dump raw data into a model and expect coherent results. I spent three weeks last year debugging a regression that was throwing out nonsense coefficients, and it turned out my date columns had been imported as text because a handful of cells contained error codes like "N/A" that looked fine at a glance. Once I stripped those out and standardized the column types, the model converged on the first try. Start by establishing a clean schema. Every column needs a defined type — integer, float, string, or date. Anything ambiguous gets flagged before you move forward. Use a simple pivot table or a quick cross-tabulation to check for empty cells, duplicates, and outlier ranges. This alone will cut your cleaning time significantly compared to running analyses and then realizing halfway through that your dependent variable has fifty percent missing values.

Quantitative Analysis Statistics Notes

When I reference these notes, I mean the actual working document — the one where you track every transformation, every assumption, every decision about which test to run and why. The notes aren't decoration. They're the reason you can reproduce your work six months later without going insane. I keep them in a single markdown or plain text file alongside the dataset. Each section covers the data source, the variables, the statistical tests applied, the output, and any deviations from the plan. Here's a structure that actually works in practice: Section 1: Data provenance. Where did the data come from, what sampling method was used, what's the sample size, and what's the date range?

Section 2: Variable definitions. Every variable with its measurement scale, coding scheme, and any recoding steps. Section 3: Cleaning log. What was removed, imputed, or transformed, and why. This should include the exact thresholds used for outlier removal. Section 4: Analytical decisions. Which tests were selected, what assumptions were checked, and what happened when assumptions were violated.

Section 5: Results. Output tables, effect sizes, confidence intervals, and p-values — not just the final summary but the intermediate diagnostics too. Section 6: Limitations and edge cases. What didn't work, what you had to compromise on, and what caveats apply to the conclusions. The fifth section is where most people skimp. They report the final t-test result and move on. But if you ran a Shapiro-Wilk test and found non-normality, then switched to a Mann-Whitney U test, that decision chain matters. Someone reading your notes needs to see the path, not just the destination.

Choosing the Right Test and Understanding What It Actually Tells You

Beginners pick tests based on what they've heard is "standard" rather than what matches their data structure. This leads to problems like running a Pearson correlation on ordinal Likert-scale data, or using a t-test when the samples are clearly paired. The difference between independent and paired samples is something you should verify before anything else, not after you've already run the analysis. A common counter-intuitive thing most people miss: a statistically significant result doesn't mean the effect is meaningful. In my experience with medium-sized datasets, p-values under 0.05 frequently correspond to effect sizes that are practically irrelevant. I once ran a chi-square test on a sample of about twelve thousand observations and got a p-value of 0.003 for a relationship between two variables where Cramer's V was 0.04. That's a tiny association that's only significant because the sample was huge. The takeaway is to always report effect sizes alongside significance tests. Cohen's d for t-tests, eta-squared for ANOVA, Cramer's V for chi-square — whatever fits your design. Another thing that trips people up is assuming normality is required for everything. It isn't. Non-parametric tests exist for a reason, but they're not just a fallback when normality fails. They have different assumptions of their own. The Mann-Whitney U test, for instance, compares distributions, not just medians. If two groups have the same median but very different variances, Mann-Whitney can still return a significant result, and calling it a "median test" would be misleading.

Handling Missing Data Without Ruining Your Analysis

Missing data is unavoidable in real-world datasets. The approach you choose depends entirely on the mechanism causing the missingness. There are three categories: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Most analysts treat everything as MCAR and listwise delete, which is lazy and often wrong. If your data is MAR — meaning the probability of missingness depends on observed variables — then multiple imputation is usually the right call. If it's MNAR, no statistical trick will fully fix it, and you need to document that limitation explicitly. I once worked with a survey dataset where roughly twenty percent of responses to one income question were missing. A quick Little's MCAR test came back significant, so the data wasn't missing completely at random. Running a complete-case analysis would have introduced selection bias because the missingness correlated with age. I used predictive mean matching with ten imputed datasets, ran the analysis on each, and pooled the results using Rubin's rules. The pooled estimate differed from the complete-case estimate by about eight percent, which is enough to change a conclusion in some contexts.

Common Pitfalls That Waste Time

Multiple comparisons without correction is probably the most frequent error I see. If you run twenty independent hypothesis tests at alpha 0.05, you should expect about one false positive purely by chance. The Bonferroni correction is conservative but simple. The Benjamini-Hochberg procedure controls the false discovery rate and is less harsh on statistical power, which makes it preferable when you're running a large number of tests. Neither is perfect, but doing nothing is worse. Harking — hypothesizing after the results are known — is another trap. You explore your data, spot an interesting pattern, and then present it as a confirmatory test. The p-value from that test is invalid because the hypothesis wasn't pre-registered. The honest move is to label it exploratory and either validate it on a holdout sample or collect new data. Another issue is overfitting in regression models. Adding more predictors always improves R-squared, but adjusted R-squared and cross-validation are better indicators of whether you're actually learning something generalizable. I use leave-one-out cross-validation for smaller datasets and k-fold with k equal to five or ten for larger ones. If the cross-validated R-squared drops by more than ten percentage points compared to the training R-squared, the model is likely overfit and needs simplification.

What This Approach Doesn't Handle Well

Quantitative analysis statistics notes and the methods behind them don't solve qualitative problems. If your research question involves understanding why people behave the way they do, statistical significance alone won't answer it. These notes are excellent for documenting what the numbers show and how they were derived, but they don't replace triangulation with other methods when the research design calls for it. Another hard limitation is causal inference from observational data. No amount of statistical control eliminates confounding in a non-experimental setting. Propensity score matching helps, instrumental variables help in specific scenarios, and difference-in-differences works when you have panel data with a clear intervention point. But these techniques come with their own assumptions, and when those assumptions are violated, the estimates can be worse than a naive regression. I've seen people run propensity score matching on data where the overlap assumption was clearly violated — the treated and control groups shared almost no common support — and report the results as if causality had been established. It hadn't. If your data has severe measurement error, quantitative methods can amplify rather than reduce the problem. Garbage in, garbage out applies with full force here. The notes should reflect the quality of the instruments used, not just the statistical output.

Practical Workflow for Running an Analysis

I usually follow this sequence now instead of the way I used to, which was much messier. First, I define the research question and the primary hypothesis. Then I inspect the raw data visually — histograms, box plots, scatter matrices — before touching any statistical test. After that, I document the variable coding and handle missing data. Then I run descriptive statistics to establish baselines. Only after all of that do I choose and run the inferential tests, checking assumptions at each step. I record the assumption checks and the decisions made when assumptions failed. Finally, I interpret the results in terms of effect size and practical relevance, not just p-values. This workflow takes longer upfront but saves time overall because you avoid the back-and-forth of re-running analyses after discovering that an assumption was violated or that the data needed recoding. In my experience, it reduces the total time from raw data to final results by about forty percent compared to the ad-hoc approach, because there are fewer rounds of revision. Keep your notes updated as you go, not at the end. Writing everything up after the fact means you'll forget why you made certain decisions, and forgotten decisions are where errors hide.