Module 3.3: Skewness,Kurtosis and Position

Leptokurtic

(lepto means "thin") are normal curves that are tall and thin, with only a few scores in the middle of the distribution having a high frequency. o Consistent scores to the mean o Low amount of variance

Mesokurtic

(meso means "middle") are normal curves that have peaks of medium height and distributions that are moderate in breadth. o Normally in shape (equally distributed) o Looks like a bell o Mahirap pag eyeballing

Platykurtic

(platy means "broad or flat") are normal curves that are short and more dispersed (broader). o Values are not concentrated in the middle and much farther away

Symmetric

- 50% lowe; 50%Higher · meaning the measures of the central tendency are approximately equal/similar

S>0

- Positively skewed

Reference point/norm

sample reference point where your score will be compared. Representative scores for the population. Allows us to compare people from different groups and different data gathering methods

Shape

shows how data are distributed

Absence of symmetry means __________

skewness

Eyeballing

we judge the data/distribution based on the graphical representation · Estimation based on graph · Looking if the shape is symmetric · Many of the statistical procedures rely on the normal distribution

Symmetric distributions

where we can use the mean safely because it represents the most frequent value.

1st Quartile

§ gitna/median of mean and lowest value

3rd Quartile-75%

§ median/gitna of the mean and highest value

Skewness

· Lack of symmetry; asymmetrical · Measure of shape how asymmetric the distribution is · When we say the distribution is symmetric- the mean,median,mode values are equal · When we are dealing with skewness the values are not equal.

Histogram/Histographs

· Used for continuous data; interval and ratio data in psychology · May values in between · Graphical representation of the frequency distribution · Unlike bar graph; Histograms are classified by intervals · The higher the bar; more frequent

Calculation of Percentile Rank

· We rank the data · Use the formula o (# of values below x/ n)100

4th Quartile

-100% § Highest value

2nd Quartile

-50% § middle/median

K

=represents the value of the percentile o P10= 10% o P85= 85%

Rule of thumb in Skewness

If the coefficient is greater than 3(regardless sign) considered as skewed. Generally, we accept values closer to 0.

S<0

Negatively skewed

Two kinds of Skewness

Negatively skewed Positively skewed

Kurtosis Coefficient

Positive-Leptokurtic Negative-Platykuric

X axis

Right side= Higher values;Left side=Lower values

S=0

Symmetric

Most real life data it approximates a normal distribution

True; · We can make assumptions and predictions

Measures of Shape

Using frequency polygons can help visualize the various shapes and forms taken by every distribution. Some distributions are symmetrical but some distributions contain extreme score in both directions (high and low). Some distributions are said to be skewed (extreme cases in one direction that the other) while variations in symmetrical distributions also differs in term of peakness (kurtosis) (Jackson, 2014).

Positive Skew

a distribution in which the peak is to the left of the center point and the tail extends toward the right or in the positive direction (Jackson, 2013). Few individuals have extremely high scores that pull the distribution to the right or positive direction. In a positively skewed distribution, the mode is having the highest frequency, the median divides the distribution and the mean is pulled on the direction of the tail (the extreme scores inflate the mean). o Longer tail at the left side o Pulling the mean to high values o The mean is greater than the median and mode. Frequent values below the mean and less frequent values above the mean

Negatively Skewed

a distribution in which the peak is to the right of the center point and the tail extends toward the left or in the negative direction. The mean is pulled toward the left by the few extremely low scores in the distribution. o Longer tail at the left side o Few (extreme) values that pulls the mean o The mean would be lower than the median, mode will be concentrated above the mean and median o Less frequent values below the mean compared to above the mean

Sometimes we base course not a particular criterion but by __________________

a reference point/norm · Just like the percentile · Usually we use that in Education

Quartile

are points that divide the distribution into quarters division in quarters

Pk

is the value that divides the lowest k% of the data from the highest(100-K)% of the data

Edges/Tails of the distribution

mas konti yung values, much farther away or less frequent.

Middle

mas madami, Average,frequent

normally distributed

most of the population would have results close the mean values of the histogram to the mean is closer

Decile

percentile ranks that divide the 100-unit scale by 10s · divided in to ten

Percentile

rank is defined as the percentage of scores that are below the score in question Position with respect to order in the sorted data set · Position of that score if we divided the score into 100 parts o Define the scores if it is lower,higher or equal idea of that score relative to the entire group

Kurtosis

refers to how flat or peaked a normal distribution is. It also refers to the degree of dispersion among the scores, or whether the distribution is tall and skinny or short and fat (Jackson, 2013). · Represents the mode, frequent/concentrated values · Referring to peak

L

represents the location of the individual score of a percentile