Week 3

Terminology of Samples

  • Population

    • A collection of people who share common observable characteristics

    • Rarely, called “universe”

  • Sample

    • Subgroup that has been selected, by using one of several methods, from the population.

    • N = size of population, n = size of sample.

  • Representativeness

    • Degree to which characteristics of the sample correspond to the characteristics of the population which the sample was chosen.

    • Sampling bias

      • Occurs when individuals who have been selected are NOT representative of the larger population, leading to skewed results and conclusions.

  • Parameter: Measurable attribute of a population

    • u = mean of population

  • Statisitcs: Numbers which explain a sample.

  • Estimation: Use of sample-based data to make conclusions about the population from which a sample has been selected.

  • Precision: extent to which the estimates derived from the sample reflect the population of interest

  • Accuracy: extent to which the estimates derived from the sample reflect systematic error/bias.

    • Systematic exclusion? Who is missing?

    • High accuracy indicates lack of bias versus low accuracy indicates error

Rationality of Sampling

  • Sampling allows valid generalizations after careful measurement of variables within a population.

  • Sampling saves a lot of money and time by finding accurate smaller groups to identify the larger group.

  • Larger the sample, the better, however can impose greater margins of error. Sample sizes require 15 people minimum to have any significance.

Types of Sampling

  • Non-probability/non-random

    • Can be samples of convenience, samples of volunteers.

    • Homogenous: chosen due to a trait possessed

    • Judgmental: Individual chosen because they seem “typical”

    • Snowball: Referrals by participants asked to identify other individuals who would fit the criteria for the study.

    • Quota: Participants selected

    • to meet specific characteristics or quotas to ensure representation of diverse groups within the sample.

  • Probability/random

    • Everyone should have the same chance of being selected, often more aligned with the population.

    • Simple random: Lottery system, chosen from a pool where each individual has an equal opportunity to be selected, minimizing bias in the sampling process.

    • Fishbowl: A method where participants' names are placed in a container and drawn randomly, ensuring everyone has an equal likelihood of being included in the sample.

    • Systematic: Every nth person is selected.

    • Stratified: Subgroups are produced, participants drawn randomly from them.

    • Cluster: random sampling of groups.

Inferiority of non-probability

  • Possible reasons to use it:

    • No complete listing of the population or the population is difficult to identify

    • Resources are limited.

    • Samples are more important.

Issues with Probability

  • Randomization decreases selection bias, however errors can arise from improper sample sizes or miscalculating probabilities, leading to skewed results that may misrepresent the population.

  • Sampling error indicated as a confidence interval +-5%

Measurements

  • Measurement is the systematic application of procedures and processes which ensure that data collected is accurate, reliable, and valid for establishing the desired outcomes in research.

Types of Data

  • Construct: concepts is incorpated into theory

Variables: constructs are measured.

  • Quantitative vs Qualitive

  • Qualitive Data lacks numerical value, and names, symbols, or numerical codes used.

Quantitative Data

  • Measures of values or counts; expressed as numbers.

  • Discrete Data: Data that have finite or countable number of values.

    • Dichotomous data = binary data

  • Continuous Data: Data which presents an infinite number of possible values within a given range, allowing for measurements that can be divided into smaller increments.

Levels of Measurement

  • Nominal: Categorical data, grouping data. Groupings mutually exclusive.

  • Ordinal: Ranked data, meaningful, hierarchical order, but measurement is not continuous.

  • Interval: Data within known and equal distance between intervals.

    • Continuous measure on the scale, levels in between attributes are measurable.

  • Ratio: Data with known and equal distance between intervals and a “0” value with absolute meaning. Continous measurements with increased attributes can be done. Multiplicative statements can be made.

Graphing

Histogram

  • graphical representation of the distribution of data

  • rectangles whose area is proportional to frequency of a variable and whose width is equal to class interval.

STEM and LEAF plot

  • Stem and leaf plot is a graphical representation of the distribution of data in which the leaf is usually the last digit (the ones digit) in number and the steam represents the number or number to the left of the last digit.

  • Double-sided steam and leaf plots allow compariosons between two different sets of data, providing a concise way to visualize and analyze the similarities and differences in their distributions.

Bar Graph

  • Chart which shows different categories and the amount in each category; Vertical is more common than horizontal.

  • Grouped bar graphs show info about subgroups in the categories.

Stacked Bar Graph

  • A stacked bar graph is a type of bar graph in which related are “stacked” on top of each other.

  • Shows subgroups in each category, but subgroyps are shown within same bar.

Line Graph

  • Graphical representation of data shown by line following points that represent the values of a variable over a continuous range, making it effective for displaying trends over time.

  • Very group at representing and comparing trends, and groups.

Pie Chart!

  • Pie chart is a circular r