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PSYC 315 > Chapter 2 - Distributions of Scores > Flashcards

Chapter 2 - Distributions of Scores Flashcards

1
Q

Is 80% a good grade?

A

relative

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2
Q

what is a distribution?

A
  • Conveys relative
    frequency with which
    values of a variable occur
    in a sample or population
  • Summarize how often
    scores occur in a data set
  • Can be conveyed in tables,
    histograms, or polygons
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3
Q

what is relative frequency

A

relative frequency = frequency of event/total # of event

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4
Q

what is the difference between histograms and bar graphs?

A

bar graphs = bars don’t touch
histograms = bars touch themselves (continuous)

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5
Q

can you calculate an average for a qualitative variable?

A

no!

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6
Q

what are frequency tables?

A

Conveys the number or
proportion of scores in a sample or
population having each value of a variable

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7
Q

define variable, frequency and proportion

A
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8
Q

what are bar graphs?

A

Graphical depiction of the
information presented in a frequency
table
* Each value represented by a bar,
heigh represents number or
proportion of scores having that value
* X-Axis shows the area of
preference
* Y-Axis shows proportion of
students choosing each of the
five areas

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9
Q

what is the difference between discrete quantitative variables and continuous quantitative variables?

A
  • Discrete quantitative variables
    are typically integers
  • E.g., There are 31 days in January ( 31 )
  • Continuous quantitative variables
    are typically real numbers
  • E.g., The class average o
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10
Q

give an example of a frequency table

A
  • Example:
  • We have data from a pop quiz
    last term
    Pop Quiz Data
    6 7 9 8 8 7 7 7 7 6
    6 6 7 8 6 7 7 8 4 7
    8 7 6 7 7 6 8 8
    5 7 10 8 8 7 10 6
    7 7 7 6
  • Our sample consists of 80 students ( n = 80 )
    5 7 * The pop quiz consisted of 10
    multiple choice questions
  • Grades on the quiz ranged
    from 0 to 10
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11
Q

what are the titles we look for in a frequency table?

A

value
f = frequency
cumulative f
p = proportion
P = cumulative proportion

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12
Q

how do we find the value?

A

value is just the different grades obtained by class

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13
Q

how do we obtain the frequency?

A

count the number of times a value was received by the students

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14
Q

how do we obtain cumulative frequency?

A

the number of scores at
or below a given
value of a variable

slide 12 to see how to calculate

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15
Q

how do we obtain proportion?

A

Divide by the number
of scores in the data
set (n)

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16
Q

how do we obtain cumulative proportion?

A

the proportion of scores
at or below a given
value of a variable
* 26 / 80 = 0.325 = 0.33

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17
Q

define percentile rank

A

Cumulative
proportion multiplied
by 100
* 0.325 X 100 = 32.5%

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18
Q

in summary, what are the 5 steps to creating frequency tables?

A
  1. Determine maximum/
    minimum scores
  2. Count the instances of
    each score (f)
  3. Determine the cumulative
    frequencies
  4. Determine the proportion (p) of scores by dividing the f by number of scores
  5. Determine the cumulative
    proportion
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19
Q

what is a histogram?

A

is a graphical depiction of the number or proportion of scores in
a set
* Different than bar graphs:
1. X-axis os placed
in its natural
ordering
2. There is no space
between the bars

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20
Q

What problems might we encounter if we tried to make a frequency table for this data? (grouped frequency tables with discrete-continuous variables)

A

It would be
enormous, with most
empty as there are
only 60 scores in this
table

21
Q

so, when should we use grouped frequency tables?

A

when we have a large
number of possible scores

22
Q

what are the first and second steps to making a group frequency tables? describe in details.

A

determine the range of scores and intervals.

First decision is about the number
of intervals and their width
* Must be the same width
* Width should be an integer
* Number of intervals depends
on the number of scores
(typically 5-20)
* Interval width depends on the
number of intervals and the
range of scores
* Range = maximum - minimum

*Range = 96.9 - 38.9 = 58
Grouped Frequency Distribution of 60 Final Grades
* Divide the range by the
number of intervals, e.g., if
we have 10 intervals, 58/10 = 5.8
* Because our interval width
ought to be an integer
(whole number), round up to 6
* Interval width ought to be
intuitive, 5 or 10 versus 6 or 9

23
Q

what is the third step to making a group frequency tables? describe in details.

A
24
Q

what is the fourth step to making a group frequency tables? describe in details.

A
25
Q

what is the difference between subjective and objective probability?

A
  • Subjective Probability expresses
    individual’s subjective judgement
    about the likelihood of something
    occurring: “I’ll probably do well on the
    exam!”
  • Objective Probability expresses the
    numerical likelihood of some event
    occurring (say flipping a coin: 50/50 chance)
26
Q

is flipping a coin a qualitative or quantitative variable?

A

qualitative variable: heads or tails

27
Q

define sampling experiment or trial

A

every time you flip the coin

28
Q

what is the proportion of successes?

A

Nsucesses/Nse (sampling experiments)

29
Q

A die has 6 sides
* If we want to count the
number of time I roll a one ( 1 )
out of sixty ( 60 ) trials, how
would I do this?
* If I roll a one six times

A

p = 6/60 = 0.1

30
Q

how is probability calculated?

A

by proportion (number between 0 and 1)
A die has 6 sides
* If we want to count the
number of time I roll a one ( 1 )
out of sixty ( 60 ) trials, how
would I do this?
* If I roll a one six times

31
Q

can a proportion be negative?

A

no!

32
Q

define an event

A
  • An Event is one or more of the
    possible outcomes of a sampling
    experiment
  • If we said the success in the last
    example was rolling a 3 or a 6,
    then the event is a 3 or a 6
  • We can compute the proportion of
    times an event occurs in the same
    way we computed the proportion of
    time an outcome occurs, e.g.:
  • 75 rolls, fourteen 3s and sixteen 6s
  • p = (14 +16) / 75 = 0.4
33
Q

what is the probability of an event?

A

the proportion of time the event would occur if the same sampling experiment were repeated infinitely many times

34
Q

true or false: “The probability of an event
is the proportion of times
the even would occur in an
infinite number of identical”
sampling experiments”

A

true!

35
Q

why should we care about statistics?

A
  • Probability intimately related to our use
    of distributions in statistics
  • Given any distribution of scores, we can define a number of events
  • “Score is greater than x”
  • “Score is less than x”
  • “Score is between x and y”
  • “Score is outside the interval x to y”
36
Q

LAWS OF PROBABILITY
1. if the probability of an event is 1.00
2. if the probability of an event is 0.00
3. if the probability exceeds the values between 0 and 1
4. the sum must be equal to X?

A
  1. the event MUST occur
  2. the event will NEVER occur
  3. not possible
  4. 1.00
37
Q

describe the OR rule

A

If you are asked the probability
of x OR y occurring, you add
the probability together

38
Q

describe the AND rule

A

if you are asked the probability of x AND y occurring, you multiply the probabilities

39
Q

define mutually exclusive events

A

cannot co-occur: a coin can come up heads or tails, but NOT both

40
Q

define independent events

A

occurrence of one event
does not affect the probability of the other
* If two coins are flipped and one comes up heads it has no affect on the results of the other coin

41
Q

define dependent events

A

occurrence of one event does affect the probability of the other
- drawing from a deck of cards without replacement (/52, /52, etc.)

42
Q

What is the probability of drawing
a heart OR face card in a single
draw from the deck? (what rule do we use: OR or AND?)

A

OR RULE
Three heart cards also have faces,
these events are not mutually
exclusive, so we need to remove
the cards we counted twice
pHeart = ( 13/52 )
pFace = ( 12/52 )
pHeart&Face = ( 3/52 )
22 / 52 = .42

43
Q

What is the probability of having
two baby boys in a row? (which rule do we use OR or AND?

A

AND RULE
pBaby1 = ( 1/2 )
pBaby2 = ( 1/2 )
( 1 / 2 ) * ( 1 / 2 ) = ( 1 / 4 ) = .25
.5 * .5 = .25

44
Q
  • What is the probability of drawing a
    queen and then a king from the same
    deck of cards? WITH REPLACEMENT
A

If the queen is put back into the deck,
then on 2nd draw there will still be 52
cards in the deck
pQueen = ( 4/52 )
pKing = ( 4/52 )
( 4/52 ) * ( 4/52 ) = .005917

45
Q

What is the probability of drawing a
queen and then a king from the same
deck of cards? WITHOUT REPLACEMENT

A

If the queen is not put back into the
deck, then on 2nd draw there will now
only be 51 cards in the deck
pQueen = ( 4/52 )
pKing = ( 4/51 )
( 4/52 ) * ( 4/51 ) = .006033

46
Q

define probability distribution

A

conveys the probability that a
randomly selected score will have a given value or fall in a given interval

47
Q

why should we care about probabilities?

A
  • Probability intimately related to our use
    of distributions in statistics
  • Given any distribution of scores, we can
    define a number of events
  • “Score is greater than x”
  • “Score is less than x”
  • “Score is between x and y”
  • “Score is outside the interval x to y”
48
Q

what is a probability density function?

A
  • Probability Density Functions: plots
    the density of scores at each value of
    a continuous variable
  • This shows a hypothetical distribution
    of heights measured in inches.
  • There are more scores around the
    centre of the distribution
  • The number of scores decreases
    as we move away from the
    center.
49
Q

define density

A
  • Density is the proportion of scores in an
    interval divided by the interval width
  • d = p / w
  • p is the proportion of scores
  • w is the width
  • For each value of x, there is a single
    density
  • The area under the curve is equal to 1

PSYC 315 (3 decks)

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