Statistics: Key Concepts & Definitions

What is the difference between a population and a sample in statistics?

A population is the entire group of individuals or objects under consideration, while a sample is a subset of the population selected for study.

Distinguish between a parameter and a statistic.

A parameter is a numerical characteristic of a population, typically unknown, whereas a statistic is a numerical characteristic calculated from a sample, used to estimate a population parameter.

What are the two main types of data, and how do they differ?

Qualitative (categorical) data describes qualities or characteristics that cannot be measured numerically. Quantitative data consists of numerical values that can be measured or counted.

List and briefly describe the four levels of measurement.

Nominal data categorizes without order; Ordinal data categorizes with a meaningful order but unequal intervals; Interval data has ordered categories with equal intervals but no true zero; Ratio data has ordered categories, equal intervals, and a true zero.

What is the primary purpose of descriptive statistics?

Descriptive statistics involve organizing, summarizing, and presenting data in an informative way, such as using measures of central tendency and spread.

What is the primary purpose of inferential statistics?

Inferential statistics use sample data to make generalizations, predictions, or inferences about a larger population, often involving hypothesis testing and confidence intervals.

Define the three common measures of central tendency.

The mean is the average value; the median is the middle value when data is ordered; the mode is the most frequently occurring value.

Name and briefly describe three measures of data dispersion or spread.

The range is the difference between the maximum and minimum values; variance measures the average squared deviation from the mean; standard deviation is the square root of the variance, indicating typical deviation from the mean.

Describe the key characteristics of a normal distribution (bell curve).

A normal distribution is symmetric around its mean, unimodal, with the mean, median, and mode all being equal. Its shape is often described as a bell curve.

What is the Central Limit Theorem?

The Central Limit Theorem states that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population's distribution.

What are the null and alternative hypotheses in hypothesis testing?

The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (Ha or H1) is the claim that researchers are trying to find evidence for.

What does a P-value represent in hypothesis testing?

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true.

What is a confidence interval and what does it communicate?

A confidence interval is a range of values within which the true population parameter is estimated to lie with a certain level of confidence. It communicates the precision and uncertainty of an estimate.

Explain the difference between a Type I and a Type II error in hypothesis testing.

A Type I error occurs when the null hypothesis is rejected when it is actually true (false positive). A Type II error occurs when the null hypothesis is not rejected when it is actually false (false negative).

What is sampling bias and why is it problematic?

Sampling bias occurs when a sample is not representative of the population, leading to skewed results and inaccurate conclusions about the population.