Key takeaways
- Describe data first: centre, spread, shape and outliers.
- Probability and distributions explain how likely different values are.
- A confidence interval gives a range of plausible values, and a p-value measures how surprising data is if there were no effect.
- Correlation does not prove causation.
- Check assumptions and sample size before trusting a test result.
What is statistics for data science?
How do I describe a dataset?
Start with the centre: mean (average), median (middle) and mode (most common). Then the spread: range, interquartile range (IQR), variance and standard deviation. Look at the shape: symmetric or skewed, with or without outliers. Use a histogram and a box plot. The median and IQR are robust to outliers, while the mean and standard deviation are not.
What is probability?
Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Key rules: for independent events, P(A and B) = P(A) × P(B). P(A or B) = P(A) + P(B) − P(A and B). Conditional probability P(A | B) is the chance of A given that B happened. Bayes' theorem updates a belief when new evidence arrives: P(A | B) = P(B | A) × P(A) / P(B).
Which distributions should I know?
| Distribution | Describes | Example |
|---|---|---|
| Normal | Symmetric bell-shaped data | Heights, measurement error |
| Binomial | Number of successes in n trials | Orders that convert out of 100 visits |
| Poisson | Count of events in a time period | Calls per hour |
| Uniform | Equal chance for all values | Random number between 0 and 1 |
| Exponential | Time between events | Time until next arrival |
In a normal distribution about 68 percent of values fall within one standard deviation of the mean, 95 percent within two and 99.7 percent within three.
Why does sampling matter?
We rarely see the whole population, so we study a sample. A sample is useful only if it represents the population; random sampling helps. Bias in sampling, such as asking only online users, leads to wrong conclusions. A larger sample reduces random error but not bias.
What is the central limit theorem?
The distribution of sample means approaches a normal distribution as the sample size grows, even if the underlying data is not normal. This is why many tests use averages and why confidence intervals work.
What is a confidence interval?
A confidence interval gives a range of plausible values for a population quantity. A 95 percent interval means that if you repeated the sampling many times, about 95 percent of such intervals would contain the true value. It does not say the true value has a 95 percent chance of lying in this one interval. Wider intervals come from smaller samples or noisier data.
How does hypothesis testing work?
State a null hypothesis (no effect) and an alternative. Choose a significance level, often 0.05. Compute a test statistic and a p-value: the probability of seeing data at least this extreme if the null were true. A small p-value is evidence against the null. It is not the probability that the null is true and it says nothing about the size or importance of the effect. Report the effect size and an interval too.
Which test should I use?
| Situation | Typical test |
|---|---|
| Compare two group means | t-test |
| Compare more than two means | ANOVA |
| Two categorical variables | Chi-square test |
| Compare proportions | z-test for proportions |
| Non-normal small samples | Non-parametric tests such as Mann-Whitney |
Check assumptions such as independence and approximate normality.
What are Type I and Type II errors?
A Type I error rejects a true null (a false positive) and has probability equal to the significance level. A Type II error fails to reject a false null (a false negative). Power is the chance of detecting a real effect, and it increases with sample size and effect size. Plan the sample size before an experiment.
What about correlation and regression?
Correlation measures the strength and direction of a linear relationship from −1 to 1. It does not show causation; a third factor or coincidence may explain it. Linear regression fits a line to predict a number from one or more variables, and the coefficients show the average change per unit. Check residuals and avoid extrapolating beyond the data.
What mistakes cause wrong conclusions?
Testing many things and reporting only the significant ones (multiple comparisons), stopping an experiment early when results look good, ignoring sample bias, confusing statistical with practical significance and using the mean for heavily skewed data.
How do I practise these ideas?
Take a small dataset, compute the mean, median and standard deviation by hand and with a tool, and plot a histogram. Draw random samples of different sizes and watch how the sample mean varies. Run a t-test between two groups, compute an interval and write one paragraph in plain words that a manager could read, including the limits of the result. Writing the paragraph is the real skill.
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