Exam 2

How to add a new variable in jamovi

double click on an empty header cell then click new data variable

data visualization

puts your data into graphical form, easier to identify patterns and data

three types of graphs

histogram, bar graph/chart, dot plot

histogram

a graph showing how many of the cases in a batch of data scored each possible value or range of values on a continuous variable, can’t reorder bars, no gaps, area is proportional to data, numerical value, bin

bar graph/chart

a graph representing catgegorial data where the height of the bar is proportional to the value it represents reorder bars, categorical variable, length is proportional to data, category

dot plot

displays individual data points as a dot along a number line or axis

histogram vs bar graph

histogram cannot be reordered bar chart can, difference in spacing, area/ length, x axis

nomical or ordinal data

bar graph or frequency dot plot

interval or ratio data

histogram or dot plot

what is the goal of graphing data distributions

what values are most common for a variable answered with measures of central tendency, how much variety or variability is there in the values are there extreme outliers

when reporting results what should accompany a measure of central tendency

a measure of variability

when to use mean

data are continuous, normally distributed and contain no outliers

when to us median

data are ordinal, data are continuous but not normally distributed, have outliers

when to use mode

data are nominal, data are continuous but you want to know the most common value

when to us range

not commonly used or reported, you want a quick shorthand for variability that gives you and indication of outliers

when to use IQR or interquartile range

always report with median, data are ordinal, data are continuous but not normally distributed (skewed) or have outliers

when to use mean average deviation M.A.D.

not commonly used or reported, small dataset that you want a quick shorthand for variability

when to use variance (sample)

data are continuous and normally distributed, you have to use it in a. formula to calculate something else (otherwise report SD)

when to use Standard deviation (sample)

you’re reporting a mean, data are continuous and normally distributed, you want the variability to be interpretable in your original units

outliers in jamavoi

gives you the row not the outlier itself

how to get a z-score from a percentage

convert percentage to proportion (move decimal two places) go to z-table use column c to report z-score

frequency table

in order with number of occurrences, uses interval or ratio type variables

grouped frequency distribution tables help to

see patterns and detect weird values

steps to making a grouped frequency table

put scores in order, combine nearby items into bins that represent a range of values (need to be an equal number of values in each bin), count frequency of each score in each bin

bins are

exclusive - each item fits in no more than one bin, equal sized - each bin has the same range, exhaustive - every item fits in a bin, outliers are included in bins, use between 5-20 bins

raw frequency tables

reflect sample size, can make it hard to compare across studies with different sample size

relative frequency tables express

frequency in proportions or percentages

formula for proportion

steps for creating a relative frequency table

put scores in order, combine nearby items into bins , count frequency of each score in each bin, take the frequency of each score in each bin, take the frequency count for each bin and divide by the total observation count to get proportions, multiple proportion column by 100 to get percentages

cumulative frequency counts

accumulated scores across bins, useful for counting scores below or above a threshold value

cumulative frequencies can also be counted in

relative proportion or percentages

cumulative frerquinces don’t make as much sense for which variable type

nominal, less helpful because you can’t say above or below

steps for creating a cumulative frequency table

put scores in order, combine items into bins, count frequency of each score in each, for the cummulative column count the frequency in the current bin, plus all those below it (running total)

histogram

is a graphical depiction of a frequency table by showing how often values in the data occur

expectations for a histogram

x-axis has all possible values, y-axis reflects frequency, increment of values on the y0axis should be equal-sized, if using bins bins should be equal, exclusive and exhaustive e

why are bins helpful for histograms

it is hard to visualize not binned data

normal distribution

a symmetrical distribution of data with a single peak and a bell shape, standard bell curve, mean median and mode are all in the same spot

skewed distribution

have many observations clumped on one-end with a tail of extreme values on the other end, mean median and mode don’t line up, skew = which way the tail points

outliers

scores that are much different from the majority of scores

graphs with more than one peak

bi-modal or multi-modal

bi-modal

two peaks

multi-modal

3 or more peaks

uni-modal

one peak

comparing distribution shapes

what do you notice, what do you wonder, what is going on

central tendency

a single number that describes the center or typical point of a distribution, the value that scores in a distribution center on

measures of central tendency

summarize the middle or most typical values for a variable mode, median, mean

what factors guide choice of what measure of central tendency to use

variable type and shape of distribution

mode

the most common value of the variable

median

the middle value in a frequency distribution

mean

the arithmetic average of all values for a variable

mode

the most common value of the variable, the only and best measure for nominal variables, complement with frequencies of each category, does not require comparison between variable values or calculation of average, could use for ordinal interval and ratio variables

modes used for describing distributions

one mode, two modes, uniform (mode not helpful), multimodal two modes

is mode the absolute peak

mode is not always the absolute peak, sometimes there is another peak that it misses

if quantitative and multimodal consider why

were different versions of a measure used, was there some procedural difference that could have created unintended groupings in the data, are there naturally occurring groups in the data that should be examined seperatley

median

the middle value in a frequency distribution the point that falls in the middle of all points when putting the data in order, the median is higher than half of the scores and lower than half the scores, does not use all of the values in the data, could use for ordinal interval and ratio scales, best for ordinal, not applicable to nominal data

what to do if there are an odd number of data points for the median

put the points in order, count the points (n+1)/2

what to do if there are an even number of data points for the median

put the points in order, count the points,, take points surrounding (n+1)/2, median is the midpoint of those two points

median is best for when

ordinal measurement, or for interval and ratio if the variable is skewed

mean

the arithmetic average of all values for a variable, does use all of the values in the data highly influenced by outliers, could use for interval and ratio scales

mean equation

we can compute mean from frequency distribution

when is mean best used

shape of the distribution for interval/ratio variable is symmetrical (not skewed) and unimodal

negative skew

mean<median<mode

positively skewed

mode<median<mean

symmetric

median=mean=mode

if nominal use

mode

if ordinal

use median

if interval or ratio

use median if distribution is skewed use mean if distribution is symmetrical

variability

how spread out a distribution is aka how different (people) are from each other

distributions with the same central tendency can have

different degrees of variability

central tendency alone is not enough

discussing only central tendency gives us an incomplete picture of the data

sources of variability

participant variability, measurement variability

participant variability

between-subject, within-subject

measurement variability

random, systematic

participant variability between different participants

students will score differently from each other on a self-report measure of extraversion ex. quarterbacks in the big ten will all have different level of average pre-game anxiety

participant variability within a given participant

the same student may fluctuate slightly in how extraverted they feel they are throughout the year ex. the same quaterback will fluctuate in their pre-game anxiety across games in the season

measurement variability/error random

the measure of a construct is randomly off from the true score of the variable so sometimes its higher and other times lower, only affects the variability around the average

measurement variability/error systematic

the measure of a construct is consistently offset from the true score so it is systemically biased, does affect the average

range

a measure of variability that says how wide the distribution is - spread, high minus low

absolute range

the difference between the smallest and largest observed values

range and distribution

range can be calculated no matter the shape of the distribution, finding the min and max values is independent of the rest of the distribution

outliers and range

range is highly susceptible to outliers

interquartile range IQR

the range of the middle 50% of values; the values between the 25% (Q1) and the 75% (Q3)

What does IQR tell us

how widespread are the observations in the middle of the distribution so it is less effected by outliers, anytime you report a median you want to report IQR

how to find the IQR

put the dataset in order, split them into 2 halves divided at the median, find the middle of each half for Q1 and Q3 IQR= Q3-Q1

IQR and normal distributions

IQR is symmetrical such that a range of Q1 to Q2 is equal to range of Q2 to Q3

skewed distributions and IQR

IQR may be asymmetric such that the range of Q1 to Q2 is different than Q2 to Q3

box and whisker plot

a graph of IQR and range which helps visualize variability and skew

whiskers on a box and whisker plot

absolute range or outlier

how to calculate an outlier on a box and whisker plot

value<Q1 - IQR*1.5 value>Q3+IQR*1.5

deviation from mean

variability can be conceptualized as how much each point deviates from the mean, how spread the data are around the mean

deviation from mean formula

observed scores - mean = deviation from mean

greater deviation from the mean means

greater spread of scores, greater variability

negative deviation or positive deviation from mean

negative=score less than mean positive=score greater than mean

deviation from mean formula

deviation = xi-x(with a line on top)

what can’t you take from a deviation from mean

can’t average to quantify overall variability because it will equal zero, mean of all deviation scores will always be zero

mean as a balance point

the points are evenly distributed around the mean, the total negative deviation will always be the same amount as the total positive deviation

how do we quantify deviation from the mean

one option is to take the absolute value of all deviation scores

absolute value

dropping the sign

mean absolute deviation

quantifies the mean of the absolute deviation, gives a metric for comparing variability, distributions with higher m.a.d. have greater spread of scores