(z-Scores, Normal Curve, Probability, and Sampling Techniques)

Z- Score

- Number of standard deviations that a score is

above (or below, if it is negative) the mean of its

distribution

- It is an ordinary score transformed so that it better

describes the score’s location in a distribution

-standardizing a score to a predetermined value (μ= 0, σ= 1)

STANDARDIZED DISTRIBUTION

- is composed of scores that have been transformed

to create predetermined values for μ and σ

- used to make dissimilar distributions comparable

THE NORMAL CURVE

- specific, mathematically defined, bell-shaped

frequency distribution that is symmetrical and

unimodal; distributions observed in nature and in

research commonly approximates it

- also called the Gaussian Distribution (Carl Friedrich

Gauss)

THE NORMAL CURVE TABLE

- table showing percentages of scores associated

with the normal curve

- also called the z Table

PROBABILITY

- the extent to which an event is likely to occur as

determined by the the fraction or proportion of

successful outcomes to all the possible outcomes

- outcome – term used in discussing

probability for the result of an experiment

(or almost any event)

-what connects the population to the sample

FRACTION:

Probability of getting Ace of Spade in a deck of card

p(ace of spade)= 1/52

PERCENTAGE:

Probability of getting three dots in a dice

p(3)= 16.67%

DECIMAL/PROPORTION:

Probability of getting a head in heads or tails

p(heads)= 0.50

RANDOM SAMPLING

- requires that each individual in the population has

an equal chance of being selected

- a sample obtained by this process is called simple

random sample

SAMPLING WITH REPLACEMENT

- keeping the probabilities from changing from one

selection to the next by returning each individual to

the population before you make a selection

ADDITION RULE

- “or rule”

- Is used when there are two or more mutually

exclusive outcomes

Example:

- Heads or tails on a single flip or a coin

- Getting a 3, 4, 5 in a single roll of dice

- You want to pick a random student from your

university. With 30% are seniors and 20% are juniors,

what is the probability of getting either a senior or a

junior?

MULTIPLICATION RULE:

- “and rule”

- It is used when figuring probability of getting both

of twoo (or more) independent outcomes

Example:

- Getting a head on the second flip of the coin?

- Getting a 5 on two throws of a dice?

- Getting two questions correct on a 4-option

multiple choice exam?

SAMPLING FRAME

- Specific list of the members of the population in

order to select a subset of that population

ELEMENT

Basic unit that

represents whatever is

Being sampled and

from which

survey data are

to be gathered

PROBABILITY SAMPLING

- uses randomization to make sure that every

element of the population gets an equal chance to

be part of the selected sample.

SIMPLE RANDOM SAMPLING

- Participants has an equal chance of getting

selected to be the part sample

STRATIFIED RANDOM SAMPLING

- divides the elements of the population into small

subgroups (strata) based on the similarity in such a

way that the elements within the group are

homogeneous and heterogeneous among the

other subgroups formed.

CLUSTER SAMPLING

- The entire population is divided into clusters or

sections and then the clusters are randomly

selected. All the elements of the cluster are used for

sampling.

Single Stage

- entire cluster is selected

randomly for sampling.

Two Stage

– first,

we randomly select clusters and then from

those selected clusters we randomly

select elements for sampling

SYSTEMATIC SAMPLING

- a probability sampling method where the elements

are chosen from a target population by selecting a

random starting point and selecting other

members after a fixed ‘sampling interval’

MULTISTAGE SAMPLING

- It is the combination of one or more methods

described above.

NON-PROBABILITY SAMPLING

- a sampling technique where the samples are

gathered in a process that does not give all the

individuals in the population equal chances of

being selected.

CONVENIENCE SAMPLING

- The samples are selected based on the availability.

PURPOSIVE SAMPLING

- Sampling technique that is based on the intention

or the purpose of study

QUOTA SAMPLING

- sampling technique wherein the assembled

sample has the same proportions of individuals as

the entire population with respect to known

characteristics, traits or focused phenomenon.

REFERRAL/SNOWBALL SAMPLING

- this technique is used in the situations where the

population is completely unknown and rare