Statistical inference

Question 1

what is the statistical cycle?

Answer 1

a cycle use to carry out a statistical investigation

Question 2

what are the stages in the statistical cycle?

Answer 2

1) research design
2) sampling
3) descriptive statistics
4) inferential statistics
5) prediction / conclluton (on the population)

Question 3

what does descriptive statistics try to answer?

Answer 3

how does the sample look like?

help describe, show or summarise data in a meaningful way

Question 4

what do inferential statistics try to answer?

Answer 4

what s happening in the population?

Question 5

what are inferential statistics?

Answer 5

techniques that allow us to use samples to make generalisations about the populations from which the samples were drawn

Question 6

what are the types of inferential statistics we are looking at?

Answer 6

• hypothesis testing

- estimation of parameters

Question 7

what are the steps involved with conducting quantitative research?

Answer 7

1) define the research hypothesis for the study
2) collect data and explain how you operationally define what you are studying and set out variable to be studied (how you measure)
3) conduct hypothesis testing and draw conclusion

Question 8

what is defining research hypothesis based on?

Answer 8

based on observation and literature review

Question 9

2) operationalising variables - why should you be clear about how you measure what we are studying?

Answer 9

• so that people are in no doubt what what we are studying
• if study repeated they will get the same or similar results (internal validity)
• determines the statistical test
• examinar assesses how you define what you are measuring

Question 10

what are examples of ways in which you can measures variables?

Answer 10

• intelligence = IQ
• company performance = ROA (return of assets)

always important to look at literature first to see whether you are going to keep the vameasures the same

need to define the variables in study such as independent and dependant

Question 11

what is a statistical hypothesis?

Answer 11

an assertion, claim or prediction concerning one or more

population perimeters

Question 12

what is a population parameter?

Answer 12

a characteristic of a population

e. g. a statistic is a characteristic of the sample
e. g. mean income of subscribers to a magazine

Question 13

how do you understand the differences of individuals in a study?

Answer 13

simply summarise the data

people in the study are the sample and larger group they represent is the population

Question 14

what is the problem of sampling error?

Answer 14

the error that occurs when observing a sample instead of the whole population

drawing conclusions from the sample to the population is never certain unless we examine the whole population

Question 15

why do we use hypothesis testing?

Answer 15

to understand whether any differences or effects discovered in the study exist in the population

establish whether a research hypothesis extends beyond those individuals examined in a single study

by takin this approach you want to generalise results to a population rather than just students in their sample

Question 16

what are the steps of hypothesis testing?

Answer 16

1) state null H then select an appropriate alternative H
2) determine the level of significance
3) make a one or two tailed prediction ]

4) compute value of the test statistic from the sample
p value

5) decision: reject null if statistic has a value in the critical regions

Question 17

what are the null and alternative hypothesis?

Answer 17

statements regarding the differences or effects that occur in the population

mutually exclusive and together exhausted

Null = assumes whatever you are trying to prove did not happen, no relationship or significance

alt = there is a relationship etc

Question 18

what is the level of significance (a) ?

Answer 18

once hypothesis have been identified then you have to find evidence and develop a strategy for declaring support for either hypothesis

calculate a probability of observing you sample results given that the null is true

if there is a 5% or less chance (0.05) then you would usually accept the alternative

Question 19

why is 5% used as level of significance rather than 1 or 10%?

Answer 19

widely used in academic research, others are used to be more confident

1% - stringent, 1 in 100 chance or it happening

Question 20

what is a one tailed hypothesis?

Answer 20

has a direction

effect is going to be negative

Question 21

what is a two tailed hypothesis?

Answer 21

do not make a choice over the direction

simply implies there will be a difference but this difference is unknown

Question 22

why is the null hypothesis usually formulated?

Answer 22

in the hope of rejecting them, we need empirical evidence to do so

Question 23

what is the central limit theorem?

Answer 23

states that the sampling distribution of the sample means approaches a normal distribution as the sample gets larger, no matter what the shape of the population distribution

as you take are samples, especially larger ones, your graph of the sample means will look more like a normal distribution

Question 24

what is an essential component of the central limit theorem?

Answer 24

average of your sample means will be the population mean

add up the means from all your samples, find the average and that average will be your actual population mean

similarly if you fid the average of all the standard deviations in your sample, you’ll find the average for population

Question 25

why is central limit theorem useful

Answer 25

help predict characteristics of a population

Question 26

what is sampling distribution of the sample means?

Answer 26

a probability distribution

consists of the means of all radom samples of size n that can be drawn from a population

Question 27

what is the standard error of means equal to?

Answer 27

standard deviation of sample population

when sample is larger >30 the standard deviation of all the possible sample means is known as the standard error