Maths And Psychology Flashcards
Bar chart
To compare sets of quantitative data
must be different groups or sets the bars cannot touch on another unless two bits of quantitative data with the same group/set
Histogram
Frequency of a set piece of data
EG lists of quantitative data that is similar
In a histogram all lines must touch and the y axis must be frequency
Scatter graph
The results of two sets of quantitative data represented as a point from each value of the x axis and y axis where they intercept
Dots must be right for both the axis to plot them
Pie chart
Percentages of data out of 100% represented in a circle using angles all percentages of data must add up to 100%
Line graph
Two sets of quantitative data in a line connected from dots along the two axis
Dots must be connected and the line must connect to the origin aka 0,0
Measures of Central tendency
Mean: all the values added together and then divided by the number of values
Median: the middle value as the scores are in arithmetic order if the middle number is two numbers then do the mean of the two numbers
Mode: commonly occurring value
If there are multiple modes list them in arithmetic order
Measures of dispersion
Range: the highest value take away the smallest value
Measures of dispersion (standard deviation)
Standard deviation = the square root of the sum of each value minus the range of each value squared over the number of values minus 1
SD=√∑(x-Mean of x)²/n-1
Levels of significance
We need to at least the 95% accurate which means the probability the results are due to chance (p) must be 5% or (p=0.05)
Statistical tests
When testing correlation use a spearman’s rho
When testing nominal independent measures data use a chi-square
When testing ordinal independent measures use a Mann Whitney U
When testing an ordinal repeated measures use a wilcoxon T
Types of data
Nominal data (catagorys)
is when you can count the number of participants who did one thing or another will fall into a category
EG males and females into the categories of comedy films and horror films if they’ve watched them
Ordinal
Results of data given the form of ordinal sometimes called ranked data your told who came first second etc
(data in order)
Interval/ ratio data
data that is more than just order
shows differnces between 1st and 2nd
and 2nd and 3rd and so on
+ if data is exact and in a unit such as seconds, feet, words remembered ect. its interval/ ratio data
Frequency table
Three columns first column is what is being The Range in ascending order
if too many values or too high range, a particular interval of data value is chosen
The second column is a tally based on it’s corresponding data
Column is the frequency which is just the number of tally marks
Frequency tables and histograms
The data is put as a range on the x-axis and the frequency is on the y-axis
A symmetric histogram is if you could the histogram down the middle the right and the left hand signs are mirror images of each other
Skewed right histogram is when the majority of the frequency of data is to the left and there is few data on the right
Skewed left is when there is a lot more frequency of data on the right and lot less on the left
Normal distribution curb on the frequency distribution graph
The mean medium Mode all occur at the same point and have the same value at the highest point in the middle
Is a bell shape and has the same shape either side of the mean the pattern of scores at exactly the same above the mean as it is below
Standard deviation and the normal distribution of frequency distribution graphs
The proportion of schools falling between the mean and 1 standard deviation above or below the mean is 34%
The proportion between 1 and 2 standard deviations above or below the mean is 13.6%
The proportion of scores 2 standard deviations above or below the mean is 2.4%
So if the mean is 15 and the standard deviation is free that means 68% scored between 12 and 18 within the one standard deviation above the mean and one standard deviation below the mean
Skewed distributions on frequency graphs
Positive skew is where most of the scores lied to the left of the x-axis with fewer scores at the right of the x-axis mean>mode
A negative skew is well most of the schools would lie on the right of the x-axis and less of the schools would lie on the left of the x axis mean<median
On skewed distributions the median mode and mean will not be in the same place
mean median mode histograms
The mode will be the highest frequency
Half of the total value then add the frequencies from each group and find the group that has the frequency that is half of the total this is the median
The mean is the middle value of each range in the x-axis Times frequency of each interval then add them all together and divided by the overall frequency
This can be used to do figure out the skew of a histogram
Ratios
If the class sizes 31 and two students in the class of autism than the ratio of students with autism to students who do not have autism is 2 : 29 and the ratio between students have autism and the class size is 2 : 31
Corolations on a scatter graph
/ positive corolation
\ negative corolation
:•: No corolation
n Curvilinear corrolation
Hypothesis for correlations :
≠ sig difference
=sig relationship
Wilcoxon T
Difference of the 1st variable and the 2nd
Rank the differences
(not any that =0)
add up ranks for - diff and + diff
the smallest of these totals = T
N= number of scores (ignore if 0 diff)
Compare in provided wilcoxon Signed ranks test table for Critical value at 0.05 lvl of significance
for either if =/< critical value = significant
ordinal (data that is ordered)
Repeated measures
Differences
Man Whitney U
Spearman’ RHO
Difference of The 2 ranks
difference²
total of all d²
Calculater value =
1-6x[total of d²]/
n(number of ppts) x (n²-1)
then compare calculated value to critical value from spearman’s rank at 0.05 lvl of significance
significant= calc value >/= critical value
Ordinal (data in order)
corrilational
Chi Square
Observed - expected
(O-E)²
(O-E)²/E
add all (O-E)²/E together =Chi Square
df= (n° rows -1) × (n° collums -1)
[for the cattagorys only]
then compare Chi square value to (lvl of sig at 0.05 at the df value to get the critical value) the critical value
chi square value >/= critical value =significant
difference
nominal (catagory data)
independant measures
Standard Deviation thurther explained
SD=√∑(x-Mean of x)²/n-1
x = score
n= number of Ppts
Curvulinear correlation
looks like: n an arc that curves rises to the peak then falls
type 1 error
false positive
A false positive
This is Where Null hypothesis may be falsely rejected
The research may falsely claim an effect exists
this is likely to happen when a p-value is to lenient such as p<0.5 or p<0.3
( rejects null hypothesis when it was actually true)
Type 2 error
false negative
A false negative
this is where a null hypothesis may be falsely accepted
the research may falsely claimed an effect does not exist
this is likely to happen on a p-value is to stringent such as p<0.01
(accept null hypothesis when actually it was false)
