STAT2550-Unit1

statistics

this involves collecting, classifying, summarizing, organizing, presenting and interpreting numerical information

experimental (or observational) unit

is an object (e.g. person, animal, thing, transaction, or event) about which we collect data

-Examples:

• Each patient in a clinical drug trial

• A smartphone used in a battery life test

• Each car tested for fuel efficiency

• A customer providing feedback in a survey

• A tree observed for growth rates in an environmental study

population

is a set of units (usually people, objects, transactions, or events) that we are interested in studying

-Examples:

• All employees in a company (In the study is about job satisfaction, workplace safety, or productivity of employees in that particular company)

• All households in a city (In the study concerns income levels, energy usage, or housing conditions of the household in that particular city)

variable

is a characteristic or property of an individual experimental (or observational) unit in the population

-Examples:

• Age of students (years)

• Income of employees (dollars)

• Gender of survey respondents

• Type of car owned (SUV, sedan, truck)

• Eye colour (blue, green, brown)

sample

is a subset of the units of a population

representative sample

exhibits characteristics typical of those by the target population

statistic

is a number that represents a property by the target population

-Examples:

• Average age of students in a sample

• Average income of employees in a sample

• Proportion of male survey respondents in a sample

• Proportion of people with SUV in a sample

• Proportion of people with blue eyes in a sample

parameter

is a number that represents a property of the whole population that can be by a statistic

-Examples:

• Average age of students in a population

• Average income of employees in a population

• Proportion of male survey respondents in a population

• Proportion of people with SUV in a population

• Proportion of people with blue eyes in a population

statistical inference

is an estimation, prediction, or some other generalization about a population based on information contained in a sample

measure of reliability

is a statement (usually quantitative) about the degree of uncertainty associated with a statistical inference

descriptive statistics

utilizes and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set, and to present that information in a convenient form

-Examples:

• Average age of employees in a company

• A chart displaying proportions of product preferences

• Table summarizing sales figures by region

Inferential statistics

utilizes sample data to make estimation, designs, predictions, or other generalizations about a larger set of data

-Examples:

• Predicting future sales based on past trends

• Estimating the average weight of fish in a lake using a sample

• Forecasting election results based on exit polls

• Testing whether a new fertilizer increases crop yield

• Estimating customer satisfaction levels using a survey

Quantitative (or numerical) data

are measurements that are recorded on a naturally occurring numerical scale

Discrete data

often takes the values as whole numbers

-Examples:

• Number of students in a classroom (e.g. 25, 30, 32)

• Number of cars owned by a family (e.g. 0,1,2,3)

• Number of goals scored in a soccer match (e.g. 0,1,2,4)

Continuous data

can take any value within a range

-Examples:

• Height of students in a class (e.g. 150.2cm, 165.8cm, 172.5cm)

• Temperature of a city over a week (e.g. 23.5^oC, 25.0^oC, 19.3^oC)

• Weight of a newborn baby (e.g. 3.2kg, 3.8kg, 4.1kg)

Qualitative (or categorial) data

are measurements that cannot be measured on a natural numerical scale; they can only be classified into one of a group of categories

nominal data

represents categories that have no inherent order or ranking

-Examples:

• Types of pets owned (e.g. dog, cat, bird, fish)

• Favourite ice cream flavours (e.g. vanilla, chocolate, strawberry)

• Eye colour of individuals (e.g. brown, blue, green)

ordinal data

represents categories with a meaningful order or ranking

-Examples:

• Education level (e.g. high school, Bachelor’s, Master’s, Ph’D)

• Fitness class levels (e.g. beginner, intermediate, advanced)

• class rankings (e.g. freshman, sophomore, junior, senior)

designed experiment

Is a data collection method where the researcher exerts full control over the characteristics of the experimental units sampled. These experiments typically involve a group of experimental units that are assigned the treatment and an untreated (or control) group

-Examples:

• Testing the effect of a new drug with control and treatment groups

• Analyzing plant growth with different fertilizers

• Comparing student performance using different teaching methods

• Measuring the effect of exercise on weight loss

• Testing the effeciency of a new machine in a factory

observational study

Is a data collection method where the individual units sampled are observed in their natural setting. No attempt is made to control the characteristics of the individual units sampled

-Examples:

• Analyzing traffic patterns by observational intersections

• Studying smoking habits and lung cancer risk

• Observing social media usage without intervention

• Analyzing rainfall and crop yields without altering conditions

• Surveying dietary habits without influencing behaviour

Simple random sampling

each unit is chosen randomly, and everyone has an equal chance of being selected

-Examples:

• Selecting students for a survey using a random number generator

• Assigning numbers to survey participants and using a random table to select samples

stratified sampling

The whole population is divided into homogeneous strata or subgroups according to a specific factor. Then, the researchers draw a random sample from the different strata

-Examples:

• Sampling employees based on job roles-managers, technicians, and sales staff

• Studying income distribution by dividing participants into income brackets

cluster smapling

The target population is divided into groups (known as clusters), and a simple random sample random sample of the groups is selected. The elements in each cluster are then sampled

-Examples:

• Dividing a city into blocks and randomly selecting blocks to survey every household within those blocks

• Randomly sampling hospitals in a region and examining all patient records within those hospitals

Selection bias

results when a subset of the units in the population is excluded so that these units have no chance of being selected I the sample

-Examples:

• Studying political opinions by polling attendees at a rally for one party

• Analyzing consumer preferences by surveying shoppers at high-end mall, ignoring lower-income groups

• Evaluating healthcare access by surveying patients at private clinics and excluding public hospital patients

nonresponse bias

results when a researcher is unable to obtain data on all units selected for the sample

-Examples:

• Sending email surveys, but only tech-savvy people respond, excluding those without internet access

• Conducting phone interviews during work hours, excluding people who are employed full time

• Mailing surveys about income, and wealthier participants decline to respond due to privacy concerns

measurement error

refers to inaccuracies in the values of the data recorded. In surveys, this kind of error may be due to ambiguous or leading questions and the interviewers effect on the respondent

-Examples:

• Using a scale calibrated incorrectly, resulting in weight measurement errors

• A poorly worded questionnaire asking respondents to rate satisfaction on a 1-5 scale without clarifying what 1 or 5 means

• Asking “How many hours do you exercise per week?” without defining what counts a exercise

unethical statistics

researchers who are aware of these problems yet continues to use the sample data to make inferences are practising