Week 8 data distribution Flashcards
What does a normal distribution look like
symmetrical and bell shaped with most scores focused towards the middle
Mean, mode and median are equal
What mathematically defines a normal distribution
mean and standard deviation
What is the range of skew
-infinity to +infinity
What is the general rule for analyzing skewness
If the z-score of skewness (skewness/standard error of skewness) is > 1.96, the data is substantially skewed
What determines direction of skew
direction of tail
What does the order of central tendency look like on a negatively skewed graph
mean, median then mode is greatest
Eg on a test, most students score well but very few low (outliers) reducing the mean
What does the order of central tendency look like on a positively skewed graph
mode, median then mean the greatest
Most data points concentrated to lower end.
Eg income levels where most people earn less but some outliers earn a lot more
Kurtosis
altitude or peak of distribution
What is the range of kurtosis
-2 (flat) to +infinity
3 types of kurtosis
- Mesokurtic
- Platykurtic
- Leptokurtic
Mesokurtic
Neutral degree
Platykurtic
flat but thick in shoulders
Wide peak
Leptokurtic
peaked, thick in Centre and tails
What is the normal curve called in kurtosis
Mesokurtic
What is general rule for analyzing kurtosis
if the z score of kurtosis aka kurtosis/standard error of kurtosis is > 1.96, then the data is significantly different from Mesokurtic
Unimodal
1 peak
Bimodal
2 peaks
Multimodel
more than 2 peaks
What could be a cause of bimodal distributions
Ptsp may be not good at study so eg take longer first try but shorter second producing vastly different scores
in non-linear transformations…
all values for a particular variable are transformed
how to non-linear transform positively moderate skewed data
take the square root of each value
how to non-linear transform positively more substantial skewed data
take the logarithm of each value
how to non-linear transform positively severe skewed data
take the reciprocal transformation for each value
what do you do first when you want to non-linear transform negatively skewed data
first reflect the score, x-1 to have a positive skew
how to non-linear transform negatively moderate skewed data
take the square root of each value
how to non-linear transform negatively substantial skewed data
take the logarithm
how to non-linear transform negatively severe skewed data
take the reciprocal
why do we transform data
bring it to a normal shape
change the measure
correcting skew for stats test
difference between non linear and linear transformations
non linear change the shape of distribution scores
linear DONT change the shape of the distribution or have an effect on stats analyses - allows us to express data in different units
how can you linear transform data
multiply or divide by a constant
add or subtract a constant
combination of both
what is the mean and SD of a normal distribution
mean = 0
SD = 1
what does the value of z tell us
how many standard deviation units a particular score is from the mean
what does a positive z score indicate
observation is greater than the mean
what does z score magnitude or absolute value tell you
how far a score or observation is from the mean
what does z-score allow us to calculate
the probability of obtaining a particular score within the distribution/area under the curve
