Descriptive Statistics Lecture 3

Study Notes

Study Designs

Descriptive statistics summarize the characteristics of a dataset, including measures of central tendency and variability.
Inferential statistics use theory to guide research and answer research questions.
Research topics and questions can come from experience, emerging information, or personal bias.
A good research question should be clear, demonstrate the purpose, be answerable, and have coherence if multiple questions are asked.

Data Collection Methods

Surveys: designing a standardized instrument to collect data, easily standardized, generalizable, and can achieve a large sample size, but subject to biases and low response rates.
Observation: direct observation of a phenomenon, allowing examination of what people do, not what they say, but can be time-consuming and biased.
Interviewing: one-on-one conversation with a participant, can be structured, semi-structured, or unstructured, allowing for alteration during data collection and non-verbal cues.

Analyzing Data

Quantitative data: answering two primary questions: 1) Is there a relationship between variables? 2) Is there a strong relationship between variables?
Qualitative data: involving coding, memoing, grouping, and reviewing to generate theory or update an existing theory.
Experimental designs: true experiments, quasi-experiments, and natural experiments, with considerations for bias, confounding variables, and blinding.

Experimental Designs

True experiments: random allocation of participants to control and experimental groups, considered the "golden standard".
Quasi-experiments: non-random assignment of participants, producing a more biased sample.
Natural experiments: naturally occurring experiments, technically not "experiments" since the researcher has no control over groups.

Mixed/Multi-Method Designs

Sequential designs: one part of the study follows the other, can be sequential explanatory or sequential exploratory.
Concurrent designs: both parts of the study occur simultaneously, can be concurrent triangulation or concurrent embedded.

Measures of Central Tendency

Mean: arithmetic average, appropriate for ratio variables only.
Median: 50th percentile, literal middle case, applicable to ratio and ordinal variables.
Mode: most common attribute/value, always applicable.

Measures of Dispersion

Range: distance between the minimum and maximum values, applicable to ratio variables, but not meaningful for ordinal variables.
Inter-Quartile Range (IQR): distance between the 25th and 75th percentiles, telling us about the middle 50% of the cases.
Standard Deviation: a measure of variation for ratio level data, summarizing how spread out the data is around its mean.

Normal Distribution and Z-Scores

The Normal Distribution: a standardized, bell-shaped curve used as a reference point.
Z-Scores: each case's value put into standardized units, representing how far away from the mean a given case is.

Examining Distributions

Reading the shape of a distribution: examining skew and kurtosis to ensure normality.
Skew: deviation from a normal distribution, either positively or negatively.
Kurtosis: examination of the peak of the distribution.
Interpreting skew and kurtosis: using histogram, skew, and kurtosis statistics to determine the shape of the distribution.

Description

Learn about descriptive statistics, which summarize and describe characteristics of a dataset, including measures of central tendency and variability. Understand how to apply descriptive statistics to real-world examples.