Descriptive and Inferential Statistics Overview

A description of a concept, its variations, units of analysis, and measurement strategy.

The entity being studied, such as individuals, groups, or countries.

Explains how a concept will be measured. Describes the process & instrument.

A tool used to measure a concept, variable, or phenomenon.

The characteristic that represents a concept, derived from data.

Example: Measuring trade between countries using trade data like imports & exports.

A concept that has several parts/aspects.

A concept with only one aspect/dimension. Simplified.

An abstract idea that helps us understand and organize things in the world. It's a building block for our understanding.

The process of defining a concept clearly and precisely, making it easier to study.

Turning a concept into something measurable, like creating a questionnaire or using existing data.

Observable and measurable characteristics of a concept.

It helps researchers define concepts clearly and precisely, making them easier to study and compare.

It allows researchers to measure concepts and collect data, enabling them to analyze and understand them.

A concept with measurable properties like trade volume, foreign investment, and number of international organizations.

A statistical test used to examine the relationship between two categorical variables (nominal or ordinal). It compares observed frequencies to expected frequencies to see if there is a significant association.

Used to test hypotheses about population means when the population standard deviation is unknown. It compares sample means to either a known population mean or another sample mean.

Compares the mean of a single sample to a known population mean.

Compares the means of two independent samples to see if they differ significantly.

Measures the strength and direction of a linear relationship between two interval-ratio variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation).

A correlation between two variables is considered statistically significant if it's unlikely to have occurred by chance in the population.

t-tests require assumptions about the data, such as random sampling, interval-ratio level of measurement, and normality of the sampling distribution.

Assumptions include random sampling, interval-ratio level of measurement, linear relationship, bivariate normality, homoscedasticity, and normality of the sampling distribution.

A conceptual definition explains a concept by defining its key characteristics, units of analysis, and measurement strategy.

A good conceptual definition clearly explains variations within a concept, identifies the entities being analyzed, and suggests a method for measuring it.

A tool used to measure a concept, variable, or phenomenon. Examples include surveys, interviews, or datasets.

Unidimensional definitions focus on one aspect of a concept, which simplifies analysis and clarifies measurement.

Multidimensional concepts have several components or aspects. E.g., globalization has economic, political, and cultural sides.

A statistical test used to determine whether there is enough evidence to reject a null hypothesis, which is a statement about the population.

They help researchers make informed decisions about their research questions, allowing them to draw conclusions about the population based on sample data.

To make abstract concepts clear, precise, and measurable, allowing researchers to study them effectively.

To transform abstract concepts into variables that can be measured, allowing researchers to collect data and analyze them.

The first step in conceptualization, where you clearly define the abstract concept you're studying.

Conceptualization defines a concept clearly, while operationalization turns it into something measurable.

It helps ensure that the concepts you are exploring are well-defined and grounded in existing knowledge, reducing ambiguity and increasing credibility.

1. Clarify the Concept, 2. Develop a Conceptual Definition, 3. Operationalize the Concept, 4. Measure the Variable

By identifying observable and measurable characteristics, concrete properties reduce ambiguity and help everyone understand the concept in the same way.

Consistent bias affecting measurements, always over- or underestimating the true value. Not due to chance, but a flaw in the instrument or data collection.

Unpredictable fluctuations in measurements, sometimes overestimating, sometimes underestimating. Caused by inconsistent factors in the measurement process.

The accuracy of a measurement instrument in capturing the intended concept. Does it truly measure what it claims to measure?

The consistency of a measurement instrument in delivering the same results under similar conditions. Reproducible results.

Rejecting a true null hypothesis. Conclude there's a difference when there isn't.

A variable with categories that can be ranked but the distance between categories is not quantifiable. Examples include socioeconomic status or attitude scales.

The most precise level of measurement where categories have equal intervals and a true zero point. Examples include income, age, or number of children.

High values on one variable are associated with high values on the other, and vice versa. For example, more time spent studying is linked to higher grades.

High values on one variable are associated with low values on the other, and vice versa. For example, increased exercise might be linked to lower body weight.

Nominal, ordinal, interval-ratio. They organize variables from least to most precise, based on their properties and what mathematical operations are allowed.

Variables can be transformed from a higher level of measurement to a lower level (e.g., age to categories), but not vice versa. This simplifies the variable but reduces detail.

Interval-ratio is the highest level, allowing for all mathematical operations due to its equal intervals and true zero point.

Sometimes, simplifying a variable by using a lower level of measurement is useful for understanding the overall trend or pattern.

No, variables cannot be transformed from a lower level of measurement to a higher level. This is because you can't create more precise data from less precise data.

Positive relationships occur when high values on one variable are associated with high values on the other. Negative relationships occur when high values on one variable are associated with low values on the other.