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SAMPLING AND INFERENTIAL STATISTICS (SAMPLING (Rationale of Sampling…
SAMPLING AND INFERENTIAL STATISTICS
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INFERENTIAL STATISTICS
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Definition : Inferential statistics is the science of making reasonable decisions with limited
information
Technique used to draw conclusions about a population by testing the data taken from the sample of that population
It includes testing hypothesis and deriving estimates
It focuses on making statements about the population
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THE NULL HYPOTHESIS
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Definition : speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false.
EXAMPLE :
QUESTION
: Do teens use cell phones to access the internet more than adults?
ANSWER :
Age has no effect on how cell phones are used for internet access.
QUESTION :
Are teens better at math than adults?
ANSWER :
Age has no effect on mathematical ability.
QUESTION :
Does chewing willow bark relieve pain?
ANSWER :
There is no difference in pain relief after chewing willow bark versus taking a placebo.
To write a null hypothesis, first start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect.
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THE ALTERNATIVE HYPOTHESIS
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Definition :
The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment
Steps in Hypothesis
Formulation of the hypotheses
Choose the appropriate test
Specify the significant level
State the decision rule
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SAMPLING
Definition
: Sampling is the selection of a subset ( a statistical sample ) of individuals from within a statistical population to estimate characteristics of the whole population.
Rationale of Sampling
Inductive reasoning is an essential part of the scientific approach
Involves taking a portion of population, observe smaller group, and then generalizing the findings to the larger population
An unrepresentative
sample is termed a biased sample
Population
What is a population?
The large group about which the generalization is made
A population consists of members of a well defined segment of people, events, or objects
Samples
What is a sample?
The small group that is observed
Purpose
Obtain information concerning to the population
Probability Sampling
Probability sampling is defined as the kind of sampling in which every element in the population has an equal chance of being selected.
When probability sampling is used, inferential statistics enable researchers to estimate the extent to which the findings based on the sample are likely to differ from what they would have found by studying the whole population
Probability sampling involves sample selection in which the elements are drawn by chance procedures. The main characteristic of probability sampling is that every member of element of the population has a known probability of being chosen in the sample
Types of Probability Sampling
Simple Random Sampling
Must use a table of random numbers to select the sample
All members of the population have an "equal and independent" chance of being included in the sample
Assign each number of the population a distinct number then use the table of random numbers to select the members of the population for the sample
Random selection for small samples does not guarantee that the sample will be representative of the population
Stratified Sampling
Define subgroups, or strata, of interest then select a specified number of subjects from each subgroup
Improves representativeness and allows you to study differences between subgroups of the population
The major advantage of stratified sampling is that is guarantees representation of defined groups in the population
Cluster Sampling
You take the sample from naturally occuring groups in your population
These natural groups are called cluster
A common application of cluster sampling in education is the use of intact classrooms as clusters
The sampling error is greater than in true random sampling
Systematic Sampling
Selection of every kth person, event, or object from a list of the population
First determine number required for sample (n), then determine total N in population
N/n yields the sampling interval to use for the entire list
Systematic sampling from an alphabetical list. For example, would probably not give a representative sample of various national groups because certain national groups tend to cluster under certain letters, and the sampling interval could omit them entirely or at least not include them an adequate extent
Steps in Sampling
Identification of the target population, the large
group to which the researcher wishes to generalize the results of the study
select the sample
NONPROBABILITY SAMPLING
used when the application of probability sampling is not feasible. Its advantages are convenience and economy.
includes methods of selection in which elements
are not chosen by chance procedures. Its success depends on the knowledge, expertise, and judgment of the researcher.
The major forms of nonprobability sampling
Convenience Sampling
Weakest of all sampling procedures, involves using available cases for a study
:Various example of convenience sampling
Interviewing the first individuals your encounter on campus, using a large undergraduate class, using students in your own classroom as a sample,or taking volunteers to be interviewed in survey research
No way to estimate sampling error
without repeating the study using
probability sampling technique
Purposive Sampling
Referred to as
judgment sampling
, sample elements judged to be typical, or representative, are chosen from the population
Purposive sampling has been useful in attitude and opinion surveys
Sample elements may be typical
now not but not typical in the
future
Quota Sampling
Selecting typical cases from diverse strata of population
Elements are drown so that the resulting sample is a miniature approximation of the population with respect to the selected characteristics
Systematic bias can result
THE SIZE OF THE SAMPLE
larger sample is more likely to be a good representative of the population than
a smaller sample.
the most important characteristic of a sample is its
representativeness, not its size.
Size alone will not guarantee accuracy
A random sample of 200 is better that a random sample of 100, but a random sample of 100 is better than a biased sample of 2.5 millon
such procedures, known as
power calculations
are, the best way to determine needed sample sizes
RANDOM ASSIGNMENT
Random Assignment
is a procedureused after we have a sample of participants and before we expose them to a treatment
Example : if we wish to compare the effects of two treatments on the same sependent variable, we use random assignment to put our available participants into groups.
THE CONCEPT OF SAMPLING ERROR
THE LAW NATURE OF SAMPLING ERRORS
The laws concerning sampling error have been derived
through deductive logic and have been confi rmed through experience.
researchers cannot predict the nature and extent of the error in a single sample, they can predict the nature and extent of sampling errors in general.
When an inference is made from a sample to a population, a certain amount of error is involved because even random samples can be expected to vary from one to another
SAMPLING ERRORS OF THE MEAN
Some sampling error can always be expected when a sample mean is used to
estimate a population mean μ
Statisticians have carefully studied sampling errors of the mean and found that they follow known laws
The expected mean of sampling errors is zero
Sampling errors are distributed in a normal or near-normal manner around the expected mean of zero
Sampling error is an inverse function of sample size
Sampling error is a direct function of the standard deviation of the population
you would find that these sample means would differ from one to another and would also differ from the population mean (if it were known)
Example
: Rohan will win less than Rs.100000 in lucky draw.
