Descriptive Statistics Lecture 3

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.