Paper 2 Flashcards
what did Karl Pearson do
developed a number for correlation between -1 < r <1§
noted with the letter R
Pearson’s Product Moment Correlation PMCC
How to find the R value 8
1) press SETUP
2) Statistics (6)
3) y=a + bx
4) Type in values
5) Press AC (Statistics y = a + bx)
6) Press OPTN
7) Press 3 (Regression calc)
8) r value = r number
what is positive correlation
as one variable increases so does the other one
what is a strong positive correlation
+ 0.5 < r < + 1
what is a weak positive correlation
0 < r < + 0.5
what is a negative correlation
as one variable increases the other decreases
what is a perfect negative correlation
r = -1
what is a perfect positive correlation
r = +1
what is a strong negative correlation
-1 < r < -0.5
what is a weak negative correlation
-0.5 < r < 0
what is no correlation
no visible trend in the data r = 0
what is a cofounder
correlation caused by a third factor
what is regression
a regression line is the line of best fit
what is extrapolation
when the value lies outside the given data range, generally unreliable
what is interpolation
when the values lies inside the given data range
what is the formula to find the regression line
y = a + bx
what is a in y = a + bx
the constant term of the value of y when x = o
what is b in y = a + bx
gradient gives the increase in y when x increases by 1 unit
what is a mean
the sum of all the values divided by how many there are
what are the pros of the mean
includes every values in the calculation
what are the cons of the mean
affected by extreme values
may not be a sensible answer
what is a median
the middle value when the data is placed in order. if there are 2 middle values, find the mean of them
what are the pros of the mean
isn’t affected by extreme values
what are the cons of the mean
doesn’t include all of the data
what is a mode
the observation that occurs most frequently
what are the pros of the mean
isn’t affected by extreme values
only average used with qualitative data
what are the cons of the mean
can be multiple modes or no modes
what is a interquartile
upper quartile - lower quartile
what is the lower quartile
look at the values below the median
what is the upper quartile
look at the values above the median
what is a standard deviation
the basic idea is to find the average from the mean
how to find the standard deviation
1) turn on frequency
2) shift SETUP
3) press down
4) statistics 3
5) press ON 1
6) statistics 6
7) 1 variable 1
8) Type in values
9) press AC
10) press OPTN
11) Press 1-variable calc
what are bar charts
for discrete data
frequency given by height of bars
what are histograms
for continuous data
frequency given by area of bars
how to calculate frequency
frequency = frequency density x width
how to draw a histograms 3
- frequency can only be used on the vertical axis when the groups have equal widths
- when the class widths are equal, subtract the class boundaries to find the class widths
- when the class widths aren’t equal divide each frequency by the corresponding class width to give frequency density
what does a normal distribution have 4
- the data follows the curve closely but not exactly
- mean median and mode
- symmetry about the curve
- 50% of values less than the mean and 50% greater
what is important the remember of the normal distribution
if the probability is less than the number read straight of the table, if the value is greater than the values minus the number form 1
what was the sample mean
the average of a set of data
how to find the sample mean of 1 Sample data
- work out z-values
- use the statistical table
- to find the probability minus one from the other
what is the standard error for a sample
standard deviation / sample size squared rooted
how to find the sample mean for a SAMPLE
work out distribution
work out z values
minus the values
what Is critical analysis
involves exploring arguments. a well constructed argument should involve:
-robust evidence
-correct reasoning
-appropriate conclusion
if an argument can’t be cleared followed it maybe because its not expressed clearly enough
what is clarity 6
- use of emotive language
- use of vague language
- what knowledge does the author assume the reader has
- is the argument contradictory
- does the author make reasonable assumption
- are too many assumptions made
what is selectivity of data
one piece of data can be convincing but a range of Data needs to considered
what is sampling and training
- in a small sample steps are taken to achieve a representative sample to draw sensible conclusions
- representative samples are used to enable testing to tale place but with minimal timing
- if a particular group was not represented in the sample then any conclusion cannot be applied to any members of that particular group
what is misleading data
- times scales and axes are starting points. this is chosen to be more effective in order to further their point
- when interpreting a graph check that what appears to be shown is actually the case. conventions are that uniform scale starting from 0 are used
what is coincidence
- if two events A and B are correlated then
- it could be coincidental
- A could cause B
- B could cause A
- a third factor could cause A and B
- when two things appear to be linked they are said to be correlated. however correlation necessarily whether there is a causal link
what is critical analysis of models
- people can be highly selective of the data used to further support their point
- once a reporter have made up their mind it is sometimes too easy to grasp supporting evidence and to ignore any contradictory evidence
how do you calculate a confidence interval for the mean
- calculate the standard error
- a 95 % confidence interval means that 0.95 lies within 1.96 x the standard error of the mean sample
where does 99 % of distribution lie
-2.58 , 2.58
where does 95% of distribution lie
-1.96 , 1.96
where does 90% of distribution lie
-1.64 , 1.64
