Stats Flashcards
(104 cards)
1
Q
What is a census?
A
Where every member of the population is measured
2
Q
Positive of census?
A
Accurate result
3
Q
Problems with census?
A
Expensive + long, may destroy population
4
Q
What are sampling units?
A
Individuals of a population
5
Q
What is a sampling frame?
A
list of sampling units
6
Q
3 types of random sampling?
A
simple random
systematic
stratified
7
Q
what is simple random sample?
A
each element has equal + calculable chance of selection, list made and numberedthen put into random number gen
8
Q
What is systematic sampling?
A
Take every kth unit (k= pop/samp size), select rand no. between 1 and k to start from
9
Q
What is stratified sampling?
A
strata rep. groups of pop
samp/pop X strata size for each group, pick randomly
10
Q
advantage of simple random?
A
bias free
11
Q
Disadvantage of simple random?
A
Needs sampling frame
12
Q
Advantage of systematic?
A
Quick to use
13
Q
Disadvantage of systematic?
A
Need sampling Frame
14
Q
Advantage of stratified?
A
Reflects population
15
Q
Disadvantage of stratified?
A
Pop. must be classified
16
Q
2 types of non random sampling?
A
Quota, opportunity
17
Q
What is quota sampling?
A
same as strata but group selected by interviewer
18
Q
What is opportunity sampling?
A
quota filled by those available at the time
19
Q
advantage of quota sapling?
A
no sampling frame needed
20
Q
disadvantage of Quota sampling?
A
Non random, potentially biased
21
Q
advantage of opportunity sampling?
A
easy/cheap
22
Q
disadvantage of opportunity sampling?
A
Unlikely to be representative of population
23
Q
What is qualitative data?
A
non numerical
24
Q
What is quantitive data?
A
numerical
25
2 types of Quantitive data?
discrete and continuous
26
When were the large dataset studies taken?
may - oct 1987 and 2015
27
What are the 5 uk weather stations?
Where are they?
Cambourne - lands end
(coast)
Hurn - dorset (coast)
Heathrow - south west
Leeming - yorkshire
leuchars - scotland (coast)
28
What are the 3 international stations?
Perth - SW Australia (coast)
Jacksonville - FL (coast)
Beijing - China
29
Important to remember about seasons in perth?
opposite to the others
30
What happened in jacksonville in the years we study?
Storms - bad ones in October
31
What does tr mean (rainfall)?
Value below **0.025mm** or negligible
32
What does n/a mean?
Not available therefore you ignore that entity from calculation
33
What is cloud cover and how is it measured?
How much of the sky is covered by cloud measured in oktas or eighths
34
How many mph per knot?
1.15 mph per knot
35
When was the great storm?
15-16 October 1987 - dad’s 18th
36
What is pmcc?
Product moment correlation coefficient - strength of correlation
37
What values can pmcc take?
Between -1 and 1 where |1| represents perfect correlation
38
What is a regression line?
Line of best fit (y=mx+c) to act as a model to better understand data
39
In the regression model
y = a+bx, what does a mean?
the value of y when x = 0
40
In the regression model
y = a+bx, what does b mean?
how much the value of y changes with x
41
how do you convert the non linear model y = abˣ to a linear one?
log y = log a + x log b
42
how do you convert the non linear model y = axⁿ to a linear one?
log y = log a + n log x
43
how do you calculate mean from summarised data?
mean = Σx / n
mean = Σfx / Σf
44
how do you calculate upper and lower quartiles and median from listed data?
LQ = n/4 term
UQ = 3n/4 term
median = n/2 term
45
what to do if quartile term is a decimal (eg. 4.5th term)?
round up, so 5th term
46
What to do if quartile term is a whole number (eg 5)?
find midpoint between next term:
so it would be the 5.5th term; in which case, this would be found by adding the 5th and 6th term together and dividing by 2
47
how do you find positions of the median and quartiles from grouped data?
LQ = n/4 entity
median = n/2 entity
UQ = 3n/4 entity
48
how do you find percentiles?
(eg the 57th)
0.57 x n entity
49
what are deciles?
10% chunks, eg the 80th centile
50
how do you find the value of the percentiles in grouped data?
use linear interpolation
51
how do you do linear interpolation?
DO NOT ROUND VALUE UP
find the class that the entity falls within and subtract the no. entities in the classes before it from the positional entity
divide this number by the number of entities in the required class.
multiply this value by class width and add to the lower bound of the class to find the exact value of the centile
52
What does linear interpolation assume?
the spread of values is equal
53
What is IQR?
Inter quartile range (UQ-LQ),
A measure of spread unaffected by extreme values
54
What is inter-percentile range?
nth percentile value - mth percentile values - less effected by exteremes
55
What is variance?
Measure of spread equal to standard deviation sqrd
σ^2 = (Σx^2) / n - x̄^2
Mean of squares - square of means
56
What is standard deviation?
Square root of variance:
Rt. ((Σx^2) / n - x̄^2) = σ
57
How does coding effect mean and sd?
If y = ax + b,
Mean = a*[orig mean] + b
Sd = a*[orig. sd]
58
What is a cumulative frequency graph and how do you use it?
Read LQ from quarter up y axis where it intersects with the graph, where x cord is LQ value;
UQ is same method but 3/4 of the way up and median is half way up
59
What are box plots?
What is the tolerance for outliers?
Show outliers, IQR, Median and max permissible values.
Tolerance for outliers is 1.5 std deviations either side of upper and lower quartiles
60
What kind of data are histograms made for and what do they look like?
Continuous data so there’s no gaps
61
How do you calculate class width and area of a histogram square?
Freq. density = freq. / class width
Area = k * freq.
62
How do you compare data sets?
1. Location (mean, median or mode)
2. Spread (IQR, range, variance, sd)
3. Make analysis in context of the question
63
In venn diagrams, what does U and n mean?
U is union - A or B or both
n is intersection - A and B, must satisfy both
64
How do you signify not in a group with Venn diagrams?
(Group) dash: A’ means not in A
65
How do probability trees relate to Venn diagrams?
Makes use of conditional probabilities:
66
What does mutually exclusive?
2 events cannot occur at the same time or one entity cannot be in the two groups simultaneously
67
What is the probability of AUB and AnB if A and B are mutually exclusive and what does the Venn diagram look like?
P(AnB) = 0
P(AUB) = P(A) * P(B)
The to circles are completely separated:
68
Can you tell if two groups are independent from a Venn diagram?
Yes, the intersection region will be the product of the probabilities in the individual circles if two events are independent
69
What does it mean for two events to be independent?
The outcome of one of vent does not effect the probability of the other event occurring
70
If 2 events are independent, what are the probabilities of AnB and A given B?
P(AnB) = P(A) * P(B)
P(A/B) = P(A)
71
Can you tell whether probabilities are conditional from a Venn diagram?
No, you can’t
72
For non independent events, what is the formula for P(B/A)?
P(AnB) / P(A) = P(B/A)
73
What is the addition law for probability?
P(AUB) = P(A) + P(B) - P(AnB)
74
What is a discrete uniform distribution?
Where the probabilities of any outcome are all equal - eg rolling a fair 6 sided die
75
What is the notation of a binomial distribution?
X ~ B (no. Trials, prob. )
76
What are the 4 indicators for using a binomial distribution?
Fixed no. Trials
Fixed prob. Of success
All trials are independent
Only 2 outcomes - either success or failure
77
What are cumulative probabilities?
Where probability requested is greater than or less than a value; thus it is a collective probability of a test statistical taking a value within bounds
78
How do you calculate binomial probabilities that are get than/les than and not equal to?
Calculators only calculate < / > or equal so just add or subtract one either way depending on requirements
79
How do you find inverse probabilities on a graphical?
Run the test with any test stat, then alter prob on graphical display
80
What kind of variable is normal distribution used for and how is it denoted?
Continuous random variables
Y ~ N (mean, std. dev. Squared)
81
What does a normal distribution look like?
A bell curve with the mean in the middle and a symmetrical drop of distribution
82
What percentage of data lies in the 1st, 2nd and 3rd standard deviation from the mean respectively?
In 1 sd, 68% of data can be found, in 2 sd.s 95% of data can be found, and in 3 sd.s 99.7% of data can be found
83
How do you find inverse probs on a graphical for normal dists?
Again, run with any test stat and alter prob in graph interface
84
What is the standard normal distribution?
Like a template for when you font have mean or sd, given by :
Z ~ N (0, 1^2)
Where 0 = mean (μ) and 1 = sd (σ)
85
What is the coding for the standard normal distribution?
(Formula with z)
Z = (Y - μ) / σ
Where y is test stat, μ is mean and σ is sd
These can be substituted in many ways or solved simultaneously
86
When can you approximate a binomial dist as a normal?
When the no. Trials is large and probability of success is close to 0.5
87
what is 𝜇 and 𝜎 in a normal dist?
𝜇 is mean, np
𝜎 is std dev, √[np(1-p)]
88
What is a continuity correction?
when approximating binomial as normal, discrete data must be converted to continuous
89
how do you do a continuity correction for ≤ and
for ≤ you must add 0.5 to the test stat as the corrected stat of say 5 takes the value 4.5 to 5.5, since it is less than **or equal to** 5 must be included on the range which becomes 0 to 5.5
for <, subtract 0.5 from the test stat to exclude the actual value
90
how do you do a continuity correction for >= and >?
for >=, subtract 0.5 from the test stat so it is includes the integer and for > you add 0.5 to the test stat
91
what is the null hypothesis?
Ho, what we assume to be true
92
What is the alternative hypothesis?
H1, what would be true if Ho is wrong
93
what is significance level?
*a* the given threshold of likeliness - how tolerant we are of the possibility of a result being correct
94
what is a one tailed test?
when H1: *P*> / < to k
95
what is a 2 tailed test?
When H1: *P* is not equal to k
here, half the sig. level so that there is some for each end
96
what is ρ and what is r?
ρ is pmcc for a population and r is pmcc for a sample
97
in correlation testing, what is Ho and H1?
Ho : ρ = 0
H1 : ρ >/< or ≠ 0
98
how do you carry out a correlation test?
- Write null and alternate hypothesis
- calculate r, pmcc from sample
- Find the critical value from the
correlation tables (formula book)
- compare CV and r; if r is closer to
|1| than CV, reject Ho and if not,
reject it
- write conclusion in context
99
What is the test stat in binomial hyp. testing?
the number of successes observed
100
what are the null and alternate hyp. in binomial testing?
P = k is Ho
P < / > / ≠ k is H1
101
how do you execute a binomial hyp test?
- Write hypotheses
- assume Ho and find P >= or <= val in question using given X~B(n,p)
- if P is less than sig level, reject Ho, if greater do not reject - conclusion in context
to find critical region, run binomial dist with any X val and change prob to sig level on graphical interface, above/below given test stat is CR
102
What is actual sig level?
on binomial hyp. tests, because of discrete distribution, inverse prob will not return the given CV so question will indicate if it wants the first test stat less than the sig level or just stat with the closest rounded prob to the level.
Actual sig level is the prob of the first/closest stat in the critical region (or sum of for two tailed)
103
What is the dist. for sample mean in normal Hyp tests?
sample mean,
X̄ ~ N (𝜇,[𝝈/√n]²)
where n is sample size
104
how do you execute a normal dist hyp test?
- state Ho:𝜇 = k and
H1:𝜇 ≠ / < / > k
- calc new sd: 𝜎/√n
- assume Ho with new sd and population mean, rum distribution
- find P (X = samp. mean)
- if P is less than sig level, reject Ho, if not, d not reject Ho
- for critical regions, run with any test stat and retrospectively change prob to test stat on graph interface.
