Samples, Populations, and the Normal Distribution Flashcards

1
Q

we need to make sure, as far as we can, that our sample is an unbiased and representative sample of our population.

A

Inferential statistics

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2
Q

we also need to make sure that our sample is

A

large enough

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3
Q

Two Conditions for Random Sampling to be satisfied:

  1. every member of the population must
    have an equal chance of being selected.
A

equi-probability

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3
Q

the “gold standard” to which other sampling techniques aspire

A

random sampling

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4
Q

Two Conditions for Random Sampling to be satisfied:

  1. the selection of any one member of the
    population should not affect the chances of any other
    being selected.
A

independence

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4
Q

Many variables that can be measured on a continuous
scale are (approximately)

Many statistical tests make the assumption that our data
are

A

normally distributed

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5
Q

represented as a line chart,
with continuous variable on the x-axis (and where the
y-axis 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.

A

histrogram

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5
Q

Random Sampling is virtually impossible

A

Volunteer sample

Snowball sampling

Purposive sampling

Convenience sampling

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6
Q

We calculate the area under the curve, which will give
the number of people, which will give the probability of
the _____of responses.

A

range

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6
Q

Most of us will never need to know the ________of
the normal curve.

A

exact equation

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6
Q

Formula for Area of Triangle

A

W x H x 0.5

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6
Q

under the curve is equal to the number of people

A

area

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7
Q

There is a formula 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 ______

A

any range of responses.

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8
Q

to make the point that the normal curve is a
theoretical curve that is mathematically generated.

A

formula

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8
Q

frequency of a given value of X*

A

big Y

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9
Q

mean of the distribution

A

µ

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9
Q

any score in the distribution

A

big X

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10
Q

total frequency of the distribution

A

N

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11
Q

a constant of 3.1416

A

π

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12
Q

a constant of 2.7183

A

e

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13
Q

The _______ goes on to infinity in each
direction.

A

Normal Distribution

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13
Q

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.

A

(Mean and
Standard Deviation)

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14
Q

There is no beginning and end to the ______ on a normal
distribution plot, at least in theory.

A

x-axis

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14
Q

In a normal distribution half of the ______will lie above
the mean and half below the mean.

A

scores

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15
This means we can use the area under the curve to find the _______ of any value or range of values.
probability
15
95.45% of cases lie within _____ of the Mean.
2 SDs
16
47.72% of cases lie between the Mean and______
-2 SDs
16
2.27% of cases lie
more than 2 SDs below the Mean
16
49.9% of cases lie between the Mean and ____
+3 SDs
17
A score that is presented in terms of the number of standard deviations above the mean is called a ____
z-score or standard score
17
A z score is a transformed score that designates how many Standard Deviation units the corresponding raw score is ______
above or below the Mean.
18
process by which the raw score is altered is called a.
Score transformation
19
To calculate a z-score, we use the formula:
z = score – mean / σ (standard deviation)
20
The z transformation results in a distribution having a ____
Mean of 0 and an SD of 1.
21
comparing scores that are not otherwise directly comparable.
important use
21
Z scores allow us to determine the ______ that fall above or below any score in the distribution.
number or percentages of scores
22
the ability to compare scores that are measured on different scales is of fundamental importance to the topic of ______
correlation
23
Z scores have the _____ as the set of raw scores.
same shape
24
Transforming the ______ into their corresponding z scores does not change the shape of the distribution.
raw scores
25
The scores do not change their _________. All that changes are the score values.
relative positions.
26
The mean of the z scores always equals____
zero
27
The scores located at the mean of the raw scores will also be at the ________
mean of the z scores.
28
The SD of z scores always equals to
1
29
A raw score that is 1 SD above the mean has a z score of
+1
30
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
31
With a smaller sample, the distribution will be
t-shaped
32
Tells us that, given some assumptions, the sampling distribution of the mean will form a normal distribution, with a large sample.
Central Limit Theorem
33
Statistical tests do not assume that the distribution of the data in the sample is
normal
34
tells us that if the distribution in the sample is approximately normal, then the sampling distribution will be the correct shape
central limit theorem
35
If the sample distribution is not normal, but the sample is large enough, then the sampling distribution will still be
normal (or t-shaped).
36
The larger the sample, the less we need to worry about whether our sample data are
normally distributed or not.
36
states that the sampling distribution of any statistic will be normal or nearly normal, if the sample size is large enough.
central limit theorem
37
The more closely the sampling distribution needs to resemble a normal distribution, the more sample points will be required.
requirements for accuracy
37
How large is "large enough"?
depends on two factors
38
The more closely the original population resembles a normal distribution, the fewer sample points will be required.
The shape of the underlying population.
39
some statisticians say that a sample size of 30 is large enough when the population distribution is roughly _____
bell-shaped
40
Others recommend a sample size of at least____
40
41
But if the original population is distinctly not normal (e.g., is badly skewed, has multiple peaks, and/or has outliers), researchers like the sample size to be even_____
larger
41
standard deviation of the sampling distribution of the mean.
Standard Error ( se )
42
The Standard Error should be affected by the_______ The bigger the sample, the closer our sample mean is likely to be to the population mean.
Sample Size
43
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