Statistical inference Flashcards
what is the statistical cycle?
a cycle use to carry out a statistical investigation
what are the stages in the statistical cycle?
1) research design
2) sampling
3) descriptive statistics
4) inferential statistics
5) prediction / conclluton (on the population)
what does descriptive statistics try to answer?
how does the sample look like?
help describe, show or summarise data in a meaningful way
what do inferential statistics try to answer?
what s happening in the population?
what are inferential statistics?
techniques that allow us to use samples to make generalisations about the populations from which the samples were drawn
what are the types of inferential statistics we are looking at?
- hypothesis testing
- estimation of parameters
what are the steps involved with conducting quantitative research?
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
what is defining research hypothesis based on?
based on observation and literature review
2) operationalising variables - why should you be clear about how you measure what we are studying?
- 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
what are examples of ways in which you can measures variables?
- 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
what is a statistical hypothesis?
an assertion, claim or prediction concerning one or more
population perimeters
what is a population parameter?
a characteristic of a population
e. g. a statistic is a characteristic of the sample
e. g. mean income of subscribers to a magazine
how do you understand the differences of individuals in a study?
simply summarise the data
people in the study are the sample and larger group they represent is the population
what is the problem of sampling error?
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
why do we use hypothesis testing?
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
what are the steps of hypothesis testing?
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
what are the null and alternative hypothesis?
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
what is the level of significance (a) ?
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
why is 5% used as level of significance rather than 1 or 10%?
widely used in academic research, others are used to be more confident
1% - stringent, 1 in 100 chance or it happening
what is a one tailed hypothesis?
has a direction
effect is going to be negative
what is a two tailed hypothesis?
do not make a choice over the direction
simply implies there will be a difference but this difference is unknown
why is the null hypothesis usually formulated?
in the hope of rejecting them, we need empirical evidence to do so
what is the central limit theorem?
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
what is an essential component of the central limit theorem?
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
why is central limit theorem useful
help predict characteristics of a population
what is sampling distribution of the sample means?
a probability distribution
consists of the means of all radom samples of size n that can be drawn from a population
what is the standard error of means equal to?
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
