1-Statistical Methods

STATS

What are statistics?

Provides foundation for evidence-based reasoning and informed decision making across diverse fields including business, govt, social, medical, and physical sciences.

2 branches of stats

Descriptive Stats

Inferential Stats

What counts as descriptive stats?

• organizing data

• summarizing data

• presenting data in an informative manner

• ex: graphs

What counts as inferential stats?

• Determining something about a population based on a sample

• Methods for making decisions/predictions and drawing conclusions about populations

Probability vs Inference

What is data?

Any collection of numbers, characters, images or other items that provide information about something.

ex:

What is population?

A collection/set of all units of interest in a study.

FINITE and INFINITE → always assume infinite

ex: literally entire pop

What is sample?

A representative subset of population

RANDOM AND NONRANDOM

ex:

What is census?

A data collection from every member of the population

ex:

What is parameter?

a numerical value that summarizes a characteristic of an entire population

ex:

What is statistic?

A numerical value that summarizes the data from a sample

What is unit/subject?

The entity form which the data is collector or observation a study

ex: people, animals, objects

What is data?

The collection of values obtained for a variable from each element in a sample.

Term hierarchy in a scenario

• population

• sample

• variable

• population parameter

• sample statistics

Types of Variables

Qualitative

Quantitative

Qualitative Variables

**Categorial

describes attributes, labels, or non-numerical entries-regarding attribute

• nominal

• ordinal

ex: car model, days of the week, zip code, type of cell phone, club you joined.

Quantitative Variables

**Numerical

measurements made on numerical data-regarding amount

• discrete

• continuous

ex: gpas, heights, income, # of text messages/day, weight

Nominal

**qualitative-variable

No rank or order, mutually exclusive-CANT HAVE RANKINGS

ex: gender, nationalities, colors, blood types

Ordinal

**qualitative-variable

Natural order-PRECISE DIFFERENCE BETWEEN RANKS ARE NOT DEFINED

ex: letter grades, ABCDEFG, education level, socioeconomic status

Discrete

**Quantitative-variables

Counted items

ex: # of students in a class, # of books on a shelf, # of languages a person speaks

Continuous

**Quantitative-variables

Measured Items

ex: age of children, height of students, weights of models, temp

Converting continuous into ordinal

Ages-quantitative

• 1, 2, 3, 3, 4, 4, 4, 5, 6,

then if you group them….

• 1-3, 4-6

NOW ITS ORDINAL

Levels of Measurement

1. Nominal level

2. ordinal level

3. interval level - temp, iq scores, credit score (lacks a zero point)

4. ratio level - height, weightm time, salary, age (has zero point

Random Sampling

Non-random Sampling

Different Methods of Sampling

1. Simple Random Sampling

2. Stratified Random Sampling

3. Clustered Random Sampling

4. Multistage Random Sampling

5. Systematic Random Sampling

6. Convenience Sampling

Simple Random Sampling

• Every combination has an equal chance of being selected in the sample

Stratified Sampling

Population first divided into non-overlapping subgroups (strata) that share similar characteristics and do simple random sampling within each subgroup.

**results in a guaranteed from each subgroup?

Clustered Sampling

Divides pop. into non-overlapping subgroups (clusters) by proximity and preform simple sampling to select clusters and sample every member in the cluster (census).

**cheaper/ easier

stratified vs clustered

stratified- separate into homo groups, simple survey each group

clustered-separate into hetero groups by proximity, sample some groups, but every person in those selected

Multistage Cluster Sampling

Like hetero cluster sampling, instead of surveying everyone in the selected clusters, a random sample of elements are chosen

**also cheaper than others

Systematic Sampling

Pick random starting point then select every nth member of population

ex: ever 3rd person

Convenience Sampling

selects individuals/objects that are the easiest to access

**not recommended- rarely represent entire population

Sampling Errors

difference between a sample statistic and the true pop parameter it aims to estimate

**because its only a subset, it may not perfectly represent entire pop.

Causes of sampling errors

• population variability

• selection bias

Examples of sampling error

• election polls

• consumer surveys

• medical studies

How can we minimize sampling errors?

• Inc. sample size

• use appropriate random sampling techniques

• stratify the sample to ensure representation of key pop. subgroups

Population Variability

**causes sampling error

if pop has high variation, it gets harder to get representative sample of pop

Selection Bias

**causes sampling error

non-random sampling techniques (convinience and voluntary response) introduces bias which increase sampling error (sample is not representative)

Non-Sampling Errors

all other types of errors that occur during the data collection, processing, or analysing

**UNRELATED TO THE SAMPLING PROCESS ITSELF

Causes of Non-Sampling Errors

• Measurement and processing errors

• response bias

• non-response bias

Examples of non-sampling errors

• surveys with leading questions

• incorrect data entry

• non-response in a study

  • only certain types of people reply to the survey (ex: satisfied customers) while unsatisfied customers dont reply

How can we minimize non-sampling errors?

• address non-response bias through follow-ups or statistical adjustments

• be cautious with anonymity

• design clear and unbiased survey questions

• ensure quality control in data processing and analysis

• train data collectors and interviewers

Measurement and Processing Errors

inaccurate measurements due to errors in data, recording, or entry

**mistakes while handling the data

Response Bias

when responders provide false or misleading answers duw to the wording of the question, social desirability, interview tone, lack of knowledge, poorly designed questions, etc.

Non-Response Bias

when significant portion of selected sample does not respond

**leads to results that dont accurately represents the pop

2 Methods of Data Collection

• Observational studies

• experimental studies

Observational Studies

• Watching and recording behavior without direct interaction

• Best for studying real world behavior

Experimental Studies

• Controlled studies to determine cause and effect relationships

• Beast for scientific research and product testing

Associated Variables

**dependent variables

When 2 variables show some connection with one another

Independent Variables

When 2 variables are not associates, there is no evident connection between the two.

Types of observational studies

• retrospective

• cross-sectional

• prospective

Retrospective

**observational study

researchers analyze previously collected data

ex: medical records, surveys, data bases

Cross-sectional study

**observational study

investigator collects all measurements

Prospective

**observational study

participants are enrolled and followed at regular intervals over extended period of time.

Response Variable

**outcome/dependent variable

outcome or effect being measured in study

Explanatory Variable

**covalent/independent variable

the variable that is believed to influence or predict the response variable

Confounding variable

external factor that affects both the explanatory and response variable

can lead to misleading conclusions

lurking variable

a hidden variable that is not included in the study but influences the observed relationship between independent and dependent variable

factors

the explanatory variables in an experiment

Types of experimental designs

• completely randomized design

• block design

• matched pairs

completely randomized design

**type of experimental design

subjects are randomly assigned to different treatment groups

Block design

**type of experimental design

subjects are divided into blocks based on a characteristic before random treatment assignment

Matched pairs

**type of experimental design

each subject is paired with another similar subject, and treatments are assigned randomly within pairs