IB Maths AI Topic 4 Definitions

The claim investigated when sample evidence is strong enough against $H_0$, written as $H_1$.

A range of values used to group continuous data, usually written as an interval such as '$40\leq x\lt 50$'.

The proportion of the variation in $y$ explained by the chosen model, with values from $0$ to $1$; higher values usually indicate a better fit.

The event that $A$ does not happen, written as $A'$, with probability $P\left(A'\right)=1-P\left(A\right)$.

The probability that one event happens given that another event has already happened, written as
$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ provided that $P(B) \neq 0$.

A running total found by adding successive values as you move through a table or list.

The number of independent pieces of information used to determine the sampling distribution of a test statistic; for $\chi^2$ independence it is $(\text{rows}-1)(\text{columns}-1)$ and for goodness of fit it is $n-1$.

A set of outcomes from the sample space.

Describes events that cannot happen at the same time, so $P\left(A\cap B\right)=0$ and $P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)$.

A diagram for grouped continuous data in which each class interval is shown by a touching bar, allowing the shape and spread of the distribution to be seen.

A statement about a population parameter or about a relationship in a population that can be tested using sample data.

Referring to the middle $50\%$ of the data, between the lower quartile $Q_1$ and upper quartile $Q_3$.

The regression curve (of a chosen model type) that minimises $SS_{\text{res}}$ for the given data set.

The expected value of a random variable; if $X \sim \mathrm{Poisson}(\lambda)$, then $E(X) = \lambda$

Using technology to fit a curved model (not of the form $y=ax+b$) to data by estimating constants so the curve matches the overall pattern of the points.

A line through a point on a curve that is perpendicular to the tangent at that point, with gradient equal to the negative reciprocal of the tangent gradient.

The default claim in a hypothesis test, usually stating no difference, no effect, no association, or that a parameter has a stated value, and written as $H_0$.

A test where $H_1$ is directional (for example, $\mu_1 \gt \mu_2$ or $\mu_1 \lt \mu_2$), so the rejection region is in one tail of the sampling distribution.

One possible result of a trial.

The probability of obtaining a result at least as extreme as the sample result, assuming $H_0$ is true; smaller values give stronger evidence against $H_0$.

Values that split ordered data into $100$ equal parts; the $p$th percentile has about $p$% of the data below it and can be estimated from a cumulative frequency graph.

Measures how likely an event is to happen, taking a value between $0$ and $1$, where $0$ means impossible and $1$ means certain.

Values that split ordered data into four equal parts; on a cumulative frequency graph with $n$ values, they are estimated at cumulative frequencies $\frac{n}{4}$ and $\frac{3n}{4}$.

The chosen cut-off for deciding whether evidence against $H_0$ is strong enough to reject it, usually denoted by $\alpha$.

The total squared error from a model, calculated as $SS_{\text{res}}=\sum\left(y_{\text{actual}}-y_{\text{predicted}}\right)^2$, used to compare how closely different models fit the same data.

A measure of fit found by adding the squared residuals for all data points, $SS_{\text{res}}=\textstyle\frac{}{}\sum\left(y_{\text{actual}}-y_{\text{predicted}}\right)^2$; smaller values indicate a closer fit to the data.

A test where $H_1$ looks for a difference in either direction (for example, $\mu_1 \neq \mu_2$), so the rejection region is split between both tails.