Descriptive and Inferential Statistics Overview

Descriptive statistics

Statistics that summarize the data on one single variable.

Univariate statistics

Descriptive statistics that run on one variable at a time.

Bivariate statistics

Descriptive statistics that describe the relationship between two variables, also known as cross-tabulation, without hypothesis testing.

Measures of distribution

Help understand how data is spread across different values. Examples include frequency and percent for nominal and ordinal variables.

Central tendency

Measures include mean, median, and mode. The mean is used for normally distributed data, while the median is preferred for skewed distributions.

Dispersion or variability

Dispersion measures include standard deviation for normally distributed data and quartiles or interquartile range for non-normally distributed data.

Frequency and percent

Reported for nominal and ordinal data.

Mean and standard deviation

Reported for normally distributed continuous data.

Median and quartiles

Reported for skewed continuous data.

Bar graphs or pie charts

Used to visualize nominal and ordinal data.

Histograms

Used to visualize continuous data, showing the distribution of data across intervals.

Inferential statistics

Used to make inferences or generalizations from a sample to a population. They test relationships between two or more variables and are used for hypothesis testing.

Null Hypothesis

Posits that there is no relationship, difference, or correlation between the variables or groups. Mathematically, it suggests that any difference or relationship in group means is zero.

Alternative Hypothesis

Suggests that there is a difference or relationship between the variables. Mathematically, it indicates that the means for the groups are not the same, or if subtracted, do not equal zero.

Scoring

Involves aggregating responses from multiple questions to measure complex constructs. This can be done by summing or averaging the scores.

Reverse coding

Sometimes necessary before aggregation in scoring.

Levels of measurement

Nominal, ordinal, interval, and ratio. Nominal is the weakest, while interval and ratio are the strongest, allowing more detailed statistical manipulation.

Ordinal variables

Variables with five or fewer categories that can be dichotomized into equal or logical groups.

Continuous variables

Variables treated as such when there are six or more categories.

Pearson's chi-square test

The inferential statistic used for a categorical independent variable (IV) and a categorical dependent variable (DV).

Pearson's correlation

The inferential statistic used for a continuous independent variable (IV) and a continuous dependent variable (DV).

Independent samples t-test

The inferential statistic used for a 2-level categorical independent variable (IV) and a continuous dependent variable (DV).

ANOVA

The inferential statistic used for a 3 or more categorical level independent variable (IV) and a continuous dependent variable (DV).

Determining significance

Involves determining the appropriate test based on levels of measurement, computing the test statistic, and examining the associated p-value.

Gold standard p-value

Typically set at 0.05 for deciding whether to reject the null hypothesis.

Significant results from a t-test

Indicate that the observed relationship or difference is unlikely due to chance, leading to the rejection of the null hypothesis.

Non-significant results

Suggest that the observed relationship or difference could be due to chance, and the null hypothesis is not rejected.

Top-down approach

Associated with deductive reasoning, starting with a theory, followed by hypothesis, observation, and confirmation.

Bottom-up approach

Linked with inductive reasoning, starting with observation, identifying patterns, formulating tentative hypotheses, and developing a theory.

Qualitative research

Uses words to describe meaning, discover phenomena, and understand experiences.

Purpose of qualitative research

To understand phenomena more deeply, generate new theories, and form fully informed hypotheses without generalizing.

Topics for qualitative research

Topics that defy quantification, attitudes and behaviors in their natural setting, and social processes over time.

Forms of qualitative data collection

Includes words, images, sounds, physical objects & artifacts, and photovoice.

Descriptive notes

Capture factual data and observations.

Reflective notes

Include the observer's thoughts, feelings, and interpretations.

Methods of taking field notes

Include paper and pencil, modern technology, and video recordings.

Level of Participation

Ranges from full participant to completely unobtrusive observation.

Role of Observer

Ranges from emic (insider perspective) to etic (outsider perspective).

Awareness in observation

Ranges from overt (participants know they are being observed) to covert (participants are unaware).

Explanation in observation

Ranges from full explanation to false explanations.

Duration of observation

Ranges from single observation to long-term, multiple observations.

Structured Interview

Scheduled, formal, with open or closed-ended questions.

Semi-structured Interview

Scheduled, formal, with open-ended questions.

Unstructured Interview

Scheduled, formal, with topics set in advance.

Informal Interview

Not scheduled, often part of participant observation.

One-on-one Interview

An in-depth interview with one person, allowing for detailed exploration of individual perspectives.

Group Interviews

Heterogeneous, unstructured format.

Focus Groups

Typically homogeneous, 5-12 people, focused topic.

Quantitative Research

Predicts and tests hypotheses.

Qualitative Research

Understands meaning.

Quantitative Data

Uses numeric data.

Qualitative Data

Uses non-numeric data like words and images.

Deductive Inquiry

Quantitative is deductive.

Inductive Inquiry

Qualitative is inductive.

Structured Design

Quantitative uses structured design.

Flexible Design

Qualitative uses flexible design.

Generalizability

Quantitative aims for generalizability; qualitative does not.

Case Study

In-depth exploration of a bounded system.

Ethnography

Participant observation and fieldwork.

Phenomenological Study

Focuses on lived experiences and bracketing.

Grounded Theory

Develops concepts and categories from data.

Mixed Methods

Combines qualitative and quantitative approaches, allowing for comprehensive analysis.

Probability Sampling

Random selection, aims for generalizability.

Non-Probability Sampling

Non-random selection, focuses on depth and context.

Convenience Sampling

Based on ease of access.

Volunteer Sampling

Participants self-select into the study.

Purposive Sampling

Selection based on specific characteristics.

Quota Sampling

Ensures representation of specific subgroups.

Snowball Sampling

Participants recruit future subjects.

Focus Groups Sample Size

Typically 5-12 people per group.

Saturation

Sample size is determined when no new information is obtained.

Homogeneity

Similar characteristics among participants, leading to smaller sample sizes.

Heterogeneity

Greater diversity among participants, requiring larger sample sizes.

Saturation in Sample Size

The point at which no new information or themes are observed in the data, indicating sufficient sample size.