MATH 1_unlocked

Data Management: The process concerned with "looking after" and processing data.
Involves:
- Looking after field data sheets
- Checking and correcting raw data
- Preparing data for analysis
- Documenting and archiving data and metadata

Ensures high-quality data for analysis, leading to correct conclusions.
Enables further use of the data in future studies and facilitates integration of results.
Leads to improved data processing efficiency, quality, and meaningfulness.

Census: Sir systematic acquisition and recording of information from all members of a population.
- Rarely used due to high costs and dynamic populations.
Sample Survey: Selection of a subset within a population to gain insights about the whole.
- Advantages:
  - Lower cost
  - Faster data collection
  - Improved accuracy due to smaller datasets.
Experiment: Conducted under controlled variables to study effects.
- Requires replication to validate results.
Observation Study: No controlled variables; relies on surveys for data collection.
- Example: Examining smoking's correlation with lung cancer.

Characteristics of a Good Survey:
- Must represent a population.
- Incorporates randomness (e.g., random number generator).
- Neutral question wording to avoid biases.
- Control for potential errors and biases.
Sampling Methods:
- Nonprobability Sampling:
  - No chance of selection for some elements; reliant on non-random criteria (e.g., convenience sampling).
  - Example: Interviewing the first person to answer the door on a street.
- Probability Sampling:
  - All elements can be selected; probability can be determined.
  - Types:
    - Simple Random Sampling: Equal selection probability. Vulnerable to sampling error.
    - Systematic Sampling: Selects elements at fixed intervals; less prone to bias, but sensitive to list order.
    - Stratified Sampling: Divides population by categories to ensure representation.
    - Cluster Sampling: Selects clusters randomly; can reduce costs but increase variability.
    - Matched Random Sampling: Pairs matched by researchers to control for variables.

Issues arise from biases and errors since some individuals are excluded from selection.
Example: Convenience sampling in supermarkets can be biased towards those who respond.

Simple Random Sampling (SRS): Selections are independent; works well for homogeneous populations but can misrepresent population makeup.
Systematic Sampling: Randomly selects elements from evenly spaced intervals, risks periodic bias based on list structure.
Stratified Sampling: Ensures representation of subgroups within the larger population, enhances accuracy when variability between strata is high.
Cluster Sampling: Cost-effective; risks bias if clusters are not representative.
Matched Random Sampling: Controls for variables by pairing participants based on specified traits.

Clearly define research purpose and treatment comparisons.
Use design techniques like blocking and randomization.
Analyze data for future hypotheses and document results.
Example: The Hawthorne Effect illustrated that behavior changed due to observation rather than conditions.

Comparing effects requires control groups; treatment groups receive specific conditions, while controls do not.
Random Assignment: Ensures treatment effects are evenly distributed across groups.
Replication: Reduces variability; findings must be repeatable by others for validation.

Confounding: Extraneous variables can lead to incorrect conclusions.
- Example: Correlation between ice cream sales and drownings due to summer.
Placebo Effect and Blinding: Placebos can falsely improve conditions; subjects aren't aware of treatment reception to reduce bias.

Completely Randomized Design: Focuses solely on one primary factor; treatments assigned randomly without considering other variables.
Randomized Block Design: Uses blocks of similar subjects to reduce variability affecting results.
Matched Pairs Design: Special case of randomized block design with pairs sharing similar attributes.

Used to determine discrepancies between expected and observed frequencies.
Two types:
1. Goodness of Fit Test: Tests sample frequency distribution against expected distribution based on theory.
2. Test of Independence: Assesses if two categorical variables are independent.

Calculate observed frequencies.
Establish expected frequencies (minimum 5).
Conduct hypothesis tests (null vs. alternative hypotheses regarding frequencies).

Researchers survey coffee drinkers against previous studies.
Statistical calculation and decision criteria defined.
Chi-square statistic is derived to draw conclusions about data alignment with expectations.

Aims to find relationships between two factors, not the strength or nature of that relationship.
Formulate hypotheses for the association test, ensuring expected counts meet the minimum requirement.

Random sample of treatments for musculoskeletal pain; expected frequencies are calculated, followed by hypothesis tests to analyze independence.

A doctor hypothesizes equal proportions of births across days.
A Chi-Square test is performed following steps similar to goodness-of-fit to validate assumptions regarding frequencies.

Statistical evidence is used to confirm or reject null hypotheses regarding population distributions.