[L3] Samples, Populations, and the Normal Distribution Flashcards
In ___, we need to make sure, as far as
we can, that our sample is an unbiased and representative
sample of our population.
Inferential Statistics
we also need to make sure that our sample is ___
enough.
large
___– the “gold standard” to which other
sampling techniques aspire.
Random Sampling
Two Conditions for Random Sampling to be satisfied:
equi-probability and independence
every member of the population
must have an equal chance of being selected.
Equi-probability –
– the selection of any one member of the
population should not affect the chances of any other
being selected.
Independence
In practice it is very
___ to carry out RS!
difficult
Random Sampling is
virtually impossible
sampling methods
Volunteer sample
Snowball sampling
Purposive sampling
Convenience sampling
The Importance of the Normal Distribution
Many variables that can be measured on a continuous
scale are (approximately) normally distributed.
* Many statistical tests make the assumption that our data
are normally distributed.
Many ___ that can be measured on a continuous
scale are (approximately) normally distributed.
variables
The area under the curve is equal to the ___
number of people
in that area.
Where we have a histogram represented as a line chart,
with continuous variable on the x-axis (and where the yaxis
represents the frequency density), we can calculate
the number of people who have any score, or range of
scores, by calculating the ____
area of the chart.
Many ____ make the assumption that our data
are normally distributed.
statistical tests
The Normal Distribution goes on to
___ in each
direction.
infinity
There is no _
_
_
__ to the x-axis, on a normal
distribution plot, at least in theory.
beginning and end
The great advantage of a normal distribution is that if you
know (or can estimate) two values
__
_ you know everything there is to know about
it.
(Mean and Standard
Deviation),
A score that is presented in terms of the number of
standard deviations above the mean is called a
__
z-score.
A score that is presented in terms of the number of
___ above the mean is called a z-score.
standard deviations
To calculate a z-score, we use the formula:
__
z = score – mean / σ (standard deviation)
A z score is a transformed score that designates how many
___ the corresponding raw score is
above or below the Mean.
Standard Deviation units
– process by which the raw score is
altered
Score transformation
The z transformation results in a distribution having a
____
Mean of 0 and an SD of 1.
Z scores allow us to determine the ____ any score in the
distribution.
number or percentages
of scores that fall above or below
Z scores allow ____ between scores in different
distributions, even when the units of distributions are
different.
comparison,
Important use –
comparing scores that are not otherwise
directly comparable.
the ability to compare scores that are measured on
___is of fundamental importance to the topic
of ___.
different scales ; correlation
Z scores have the ___ as the set of raw scores.
Transforming the raw scores into their corresponding z
scores does not change the shape of the distribution.
same shape
The scores do not change their __. All that
changes are the ___
relative positions; score values.
The mean of the z scores always equals ___. The
scores located at the mean of the raw scores will also be
at the mean of the z scores.
zero
The SD of z scores always equals to __
1
_distribution of
means from a set of samples. It is a listing of all the
values the mean can take, along with the probability of
getting each value if sampling is random from the null hypothesis
population.
Sampling distribution of the mean –
- Tells us that, given some assumptions, the sampling
distribution of the mean will form a ____with a large sample
Central Limit Theorem; normal distribution,
With a smaller sample, the distribution will be_
t-shaped.
Statistical tests do not assume that the distribution of the
data in the sample is ___.
normal
Instead, it assumes that the ___ in the population is normal
sampling distribution of the
sample means
The CLT tells us that if the distribution in the sample is ___, then the sampling distribution
will be the ___
approximately normal; correct shape.
If the sample distribution is not normal, but the sample is
large enough, then the sampling distribution will still be
normal __
(or t-shaped)
The ___ the sample, the __ we need to worry about whether our sample data are normally distributed or not.
larger; less
___
_
– standard deviation of the
sampling distribution of the mean.
Standard Error ( se )
The Standard Error should be affected by the
___
Sample Size.
The bigger the sample, the closer our sample mean is likely to be to the ____
population mean.
– to make the point that the normal curve is a
theoretical curve that is mathematically generated.
Formula
We calculate the area under the curve, which will give the
number of people, which will give the ___
probability of the
range of responses.
Formula for Area of Triangle
- W x H x 0.5
Probability of scores =
area of the small triangle divided
by the area of the large triangle
There is a ___ that we use to calculate the area under
the normal curve, for any value taken from the normal
distribution, and we can use this to calculate the
probability of any range of responses.
formula
This means we can use the area under the curve to find the
___
probability of any value or range of values.
In a normal distribution ___ of the scores will lie above
the mean and ___ below the mean.
half, half
If we take a sample from a population and calculate the
mean for that sample, we are likely to find a value close
to the mean for the ___.
population
- It is very ____ that we will hit the true (population)
mean and we might, if we are very unlucky, find a value
far from the true (population) mean.
unlikely
We are just as likely to ___ the population
mean as we are to overestimate the population mean.
underestimate
This indicates that the mean is ___.
unbiased
The _____states that the sampling
distribution of any statistic will be normal or nearly
normal, if the sample size is large enough
central limit theorem
How large is “large enough”? The answer depends on two
factors.
- Requirements for accuracy.
- The shape of the underlying population.
The more closely the
sampling distribution needs to resemble a normal
distribution, the more sample points will be required.
Requirements for accuracy.
The more
closely the original population resembles a normal
distribution, the fewer sample points will be required.
The shape of the underlying population.
if there is a lot of
variation in the sample, there will be more uncertainty in
the sample, so there will be more uncertainty about the
population mean.
Amount of Variation in Sample –
: contains the z score.
Column A
lists the proportion of the total area between
a given z score and the mean.
Column B:
: lists the proportion of the total area that
exists beyond the z score.
Column C
