Notes For Statistics

Question 1

What is statistics?

Answer 1

A range of techniques and procedures for analyzing, interpreting, displaying and making decisions based on data.

Question 2

Why study statistics?

Answer 2

For objectively interpreting information and communicating results and research conclusions.

Question 3

Types of variable?

Answer 3

Independent variable and dependent variable
Quantitative and qualitative variable
Discrete variables and concrete variables

Question 4

What is independent variable?

Answer 4

Which is manipulated by the experimenter.

Question 5

What is dependent variable?

Answer 5

On which effect of independent variable is observed.

Question 6

What is quantitative variable?

Answer 6

Variables measured in terms of numbers.

Like height, weight, age etc.

Question 7

What is qualitative variable? What is it’s other name?

Answer 7

Express a qualitative attribute like hair colour, favourite movie etc.
No numerical ordering
Also called “categorical variables”

Question 8

What is discrete variable?

Answer 8

Possible scores are Discrete points on a scale (Discrete points = exact points)

Ex- no. Of children in a house can be 1 or 2 or 6
Not 1.5 or 1.6 etc…

Question 9

What is concrete variable?

Answer 9

Scale is continuous and not made up of discrete steps. We can have decimals here.
Ex- time to complete race could be 5.98 min or 6.75min etc..

Question 10

What are levels of measurement?

Answer 10

It is measurement of dependent variable

Question 11

To measure dependant variable there are various procedures and these procedures can be classified using a few _________, which are called “___” or”___”.

Answer 11

Categories
Scale-types
Scales

Question 12

What are types of scales?

Answer 12

There are 4 types of scales
# nominal scales
# ordinal scales
# interval scales
# ratio scales

Question 13

What are nominal scales?

Answer 13

#Simply naming or categorising responses from a data. Ex- you are recording favourite colour of various people. So you make a category as favourite colour and then under that you write favourite colour of different people.
# it has no ordering amongst responses. Ex- if classifying people according to their favourite colour then no sense in putting red before green or blue etc.
# it is the lowest level of measurement.

Question 14

What are ordinal scales?

Answer 14

# here our responses are ordered unlike nominal scales
# it allows comparisons between responses or of the degree to which 2-subjects possess the dependent variable. Example measuring consumer satisfaction with their products, scale of measuring the feeling- very dissatisfied, somewhat dissatisfied, somewhat satisfied, very satisfied. 
# scale is highly subjective as people may have different meanings to what different options mean like difference between one person to another about somewhat satisfied.
# it has no equal interval like there is nothing in-between of somewhat satisfied and somewhat dissatisfied.

Question 15

What are interval scales?

Answer 15

Numerical scales in which intervals have same interpretations throughout different people or places. Ex- difference between 90° and 80° will be 10° throughout. This is called having Equal intervals.

This scale does not have a true zero point. Ex- 0° does not represent complete absence of temperature.

Question 16

What are ratio scales?

Answer 16

This is the most informative scale.
# has categories, is ordered, has equal intervals
# also has true zero point (absence of quantity being measured)
Ex- Kelvin scale has a absolute zero
Amount of money you have left can be zero

Question 17

What level of measurement is used for psychological variables? And which is not?

Answer 17

Ordinal scale, nominal scale and rating scale ( like rate your feelings from 1 to 5 or 5point scale)

Ratio scale is not used because psychological characteristics can never be zero.

Question 18

What is population or population of interest?

Answer 18

Population is the collection of all people who have some characteristics in common. Population of interest includes specific groups of people who we want to study.

Question 19

Difference between population and sample?

Answer 19

In statistics we rely on a sample that is a small subset of a larger set of data used to draw inferences about the larger set.
The larger set us called as the population.

Question 20

What is the most crucial thing while choosing a sample?

Answer 20

That the sample is not over-representation of any one type of citizens.
If sample isn’t representative, a possibility of sampling bias occurs (means that our conclusions only apply to our sample and not generalisable to the full population)

Question 21

Name various sampling techniques.

Answer 21

# simple random sampling
# stratified sampling
# convenience sampling

Question 22

What is simple random sampling?

Answer 22

Most straightforward sampling strategy
Requires every member of the population to have an equal chance of being selected into a sample. And selection of one member must be independent of the selection of every other member ( if ram is selected from village one then Ramu of village one can also be selected... their selection is not dependent on eachother)
# chooses a sample by "pure chance"

Question 23

What is stratified sampling?

Answer 23

It is more of a complex sampling and can make the sample more representative.
# can be used when the population has a no. Of distinct "strata" or groups. Ex- a researcher wants to find what students of a particular college think about capital punishment but later finds That there are two types of students there one from morning classes and second have evening classes, so to have representation of both the groups in the research 50% from Am classes and 50% from pm classes students are choose randomly.
In this sampling first members who belong to each group are identified and then randomly sample from each of those subgroups in such a way that the sizes of the subgroups in the sample are proportional to their sizes in the population. Ex- if in the above example PM students are less than the Am students then in the sample too Am students should be more than Pm students.

Question 24

What is convenience sampling?

Answer 24

It’s easy to use and is usually followed up with a representative sample.
Ex- if we begin research in a completely unstudied area, we may take a short cut to quickly gather data and get a general idea of how things work through a small sample before fully investing a lot of time and energy into a well-designed research.

Question 25

What is random sample?

Answer 25

Sample in which every member of the population has an equal chance of being selected.

Question 26

Why do sample size matters?

Answer 26

Only a large sample size makes it likely that our sample is close to representative of the population.

Question 27

What are types of research designs?

Answer 27

Choice of research design is determined by the research question and logistics involved.
But in general there are three types of research designs:
# experimental designs
# quasi-experimental designs
# non- experimental designs

Question 28

What is experimental designs?

Answer 28

Experiment is defined by the use of random assignment to treatment conditions and manipulations of the independent variable.
Ex-
A clinical researcher wants to check if newly developed drug is effective in treating flu. She randomly samples 40 flu patients at several local hospitals and randomly assigns each one to two conditions (group A receives the new drug and group B receives a placebo). She measures symptoms of all participants after one week to check if any differences exist between the two groups.

Question 29

Difference between random sampling and random assignment?

Answer 29

Random sampling is thoughtful and scientific
Whereas
Random assignment is absolutely random

Random sampling is used for research to be representative of the population.
Whereas
Random assignment is used for research to be a true experiment.

Both if these help in eliminating the potential for sample Bias.

Question 30

What is quasi-experimental designs?

Answer 30

It involves manipulating independent variable but not randomly assigning people to groups. Random sampling may be sometimes possible but not random assignment. Involves getting as close as possible to the conditions of a true experiment.
Used because=
It may be unethical to deny potential treatment to someone. And it may be impossible to randomly assign people to groups.

Ex-professor teaching 1 class with traditional way and the other class with the new way here teaching method is manipulated but random sampling is not possible since students choose to enroll in course and they cannot be forced to study the subject without their will.

Question 31

What is non-experimental designs?

Answer 31

Also called “correlational research”
Involves observing things as they occur naturally and recording our observations as data.
It’s benefit is that it reflects reality as it actually exists.
Disadvantage can be subjectivity or researcher bias.

Question 32

What are types of statistical analysis?

Answer 32

Statistics used to interpret data
# descriptive statistics
# inferential statistics

Question 33

What is descriptive statistics?

Answer 33

In this we use numbers to summarize and describe data.
Data refers to information that has been collected from an experiment, a survey, etc…
Data is plural and datum is singular
Do not involve generalizing on data at hand.
Ex- if we analyse average salaries of various occupations in New Delhi then we will use descriptive stats.
Sampling error is tiny discrepancy between the population and sample selected (even best sample will somewhat off from the full population)

Question 34

What is inferential statistics?

Answer 34

Here they tell us how our data behaves.
Help is generalize our sample to the population
There are many types of inferential statistics.

Question 35

mathematical notations

Basics of summation notation

Answer 35

Refer to notes