Statistics Overview: Descriptive vs Inferential

Summarizing and presenting data easily understood.

Drawing conclusions about a population from a sample.

Summarize data, identify patterns, compare groups, present findings clearly.

Estimate population parameters, test hypotheses about populations.

Descriptive focuses on the data observed, Inferential aims for broader population conclusions.

Used in Inferential Statistics - Distribution of sample statistics.

Summarizing survey results, like percentages, average ages

The process of defining a concept clearly and precisely for research purposes.

The process of turning abstract concepts into measurable variables for research.

Abstract ideas that help us understand phenomena in the world.

Characteristics of a concept that are observable and can vary.

A clear description of a concept and its measurable properties.

Identifying the essential observable and variable characteristics of a concept.

Concrete, observable properties of a concept used to study it.

Identifying the concrete and observable properties of a concept.

Formulating a clear definition of the measurable properties of the concept.

Used for skewed distributions or outliers, providing a more accurate representation of center and spread.

A theoretical model used to represent the distribution of naturally occurring data, forming a bell-shaped curve.

The normal curve is a theoretical construct, not a perfect fit for any real-world data distribution.

The normal curve is symmetrical, meaning both sides mirror each other. The mean, median, and mode all coincide at the center.

The normal curve has one peak, indicating that one value occurs most frequently.

The normal curve is used in both descriptive and inferential statistics, helping to understand and interpret data distributions.

Another name for the normal curve, named after German mathematician Carl Friedrich Gauss.

In skewed distributions, the mean is pulled towards the tail, while the median remains a more stable representation of the center.

The IQR (interquartile range) is a measure of spread for the middle 50% of the data. It's less affected by outliers.

Reporting multiple measures of central tendency and dispersion provides a more comprehensive picture of the data.

A sampling method where every individual in the population has a known and non-zero chance of being selected for the sample.

The degree to which a sample reflects the characteristics of the population it represents.

The difference between the results obtained from a sample and the actual characteristics of the population.

As the sample size increases, the sample mean gets closer to the true population mean.

A measure of how much the sample mean is likely to vary from the true population mean.

Samples are subsets of a population used in research because studying the entire population is often impractical, time-consuming, and expensive.

A technique used when representativeness is not a primary concern or resources are limited. Findings from the sample cannot be generalized to the population.

The most basic probability sampling technique, where every element in the population has an equal chance of being chosen for the sample.

The number of cases included in a sample. It plays a crucial role in drawing meaningful conclusions from data.

The ability to apply findings from a sample to the entire population.

The entire group of individuals or items that are of interest in a research study.

A rule saying that as you take larger samples, the distribution of sample means will become a normal (bell-shaped) curve, even if the original population wasn't normal.

A way to choose a sample where every person has a known chance of being selected, ensuring a representative sample of a population.

It allows us to generalize findings from a sample to a larger population. If not used, the results may not be representative and can't be applied to the whole group.

A characteristic or feature that can change or vary from one individual or case to another.

Descriptive statistics: Summarizes and describes data. Inferential statistics: Uses sample data to make inferences about a larger population.

A measure is valid if it accurately captures the concept of interest, minimizing systematic and random errors.

A measure is reliable if it consistently produces similar results over time and across different situations.

Rejecting a true null hypothesis, concluding there's an effect when there isn't.

Failing to reject a false null hypothesis, missing a real effect.

The probability of making a Type I error, typically set at 0.05 or 0.01.

Lowering the alpha level, making the critical region smaller and requiring more stringent evidence to reject the null hypothesis.

A process involving stating the null hypothesis, selecting a sampling distribution, establishing a critical region, calculating a test statistic, and making a decision to reject or fail to reject the null.

A statement of no relationship or effect between variables.

The area in the sampling distribution where a test statistic would lead to rejecting the null hypothesis.

A value calculated from the sample data that summarizes the evidence against the null hypothesis

A statistical method that examines the relationship between one dependent variable and multiple independent variables.

A standardized process used for testing hypotheses in research.

A statement that there is no difference or relationship between variables.

The alternative explanation that the researcher aims to support.

The probability of making a Type II error. It represents the chance of failing to detect a real effect or difference.

Type II errors can occur due to small sample sizes, weak effect sizes, or high variability in the data.

Type I errors are considered more serious than Type II, especially when false positives cause harm.

These statistics aim to represent the 'typical' or 'average' value in a dataset.

The most frequently occurring value in a dataset.

The middle value in an ordered dataset.

The average value, calculated by summing all values and dividing by the number of values.

The choice depends on the data type (nominal, ordinal, interval/ratio) and the distribution's shape.