Inferential Statistics Intro Continued

Vocabulary and terminology flashcards covering inferential statistics, normality testing, hypothesis definitions, and data visualization tools based on the lecture transcript.

Null Hypothesis ($H_0$)

A statement that statistical significance or difference does not exist between two or more populations or groups.

Alternative Hypothesis ($H_1$ or $H_a$)

A statement that a phenomenon is likely occurring due to non-random causes and not just by chance.

Parametric Test

A statistical test that uses complete information about population parameters, assumes a normal distribution, and is applied to metric scales (interval or ratio) using the mean as a measure of central tendency.

Non-Parametric Test

A statistical test used when population parameters are unknown or not available; applied to nominal or ordinal scales and uses the median as a measure of central tendency.

Standard Deviation ($\sigma$)

The square root of the sum of the squared deviations divided by the number of values, quantifying the dispersion or variability of data relative to the mean.

Normal Distribution

A symmetrical distribution around the mean where data is divided into standard deviations or sigma values.

$1σ$ ($1$ Standard Deviation)

In a normal distribution, there is a $68.2\%$ chance that a random sample will sit within this range from the mean.

$2σ$ ($2$ Standard Deviations)

In a normal distribution, there is a $95.4\%$ chance that a random sample will sit within this range from the mean.

$3σ$ ($3$ Standard Deviations)

In a normal distribution, there is a $99.7\%$ chance that a random sample will sit within this range from the mean.

Confidence Interval (CI)

The range in which the true mean of a population lies with a certain probability, commonly set at $95\%$ or $99\%$, derived from a sample set.

Z-values

Standard numbers used as input for confidence interval calculations that are obtained from a look-up table.

Independent Variable

In an experiment, this is the cause (e.g., diet or treatments) being investigated.

Dependent Variable

In an experiment, this is the effect (e.g., weight or health) that depends on the cause/independent variable.

Shapiro-Wilk Test

A statistical test to evaluate data normality that is most appropriate for small sample sizes of less than $50$ samples.

Kolmogorov-Smirnov Test

A statistical test used for evaluating data normality in larger sample sizes where $n \geq 50$.

Quantile-Quantile (Q-Q) Plot

A visual, scientific approach to determine normality by plotting theoretical quantile values of a normal distribution against actual observed values; a straight line indicates normal distribution.

P-value < $0.05$

Indicates moderate evidence to reject the Null hypothesis; in normality tests, it means the data is non-normally distributed.

P-value > $0.05$

Indicates we accept the Null hypothesis; in normality tests, it means the data is normally distributed.

P-hacking

Altering the statistical tests used specifically to obtain a significant result, which is considered scientific misconduct.

Interquartile Range (IQR)

Also called the midspread or middle $50\%$, it is the difference between the $75\text{th}$ and $25\text{th}$ percentiles of a rank-ordered data set.

Whiskers

Lines displayed on a Box plot that generally represent $1.5 \times \text{IQR}$.

n.s.

A notation used in data presentation to indicate that a result is non-significant.