Flashcards in Chapter 5- Other Descriptive Statistics Deck (25):
Why would someone giving you the statement "I got a 95 on my math exam!" be statistically meaningless to you?
It doesn't tell us anything. If it was out of 100 that's great! You aced it! But if it was out of 200? Wow, you failed.
But if they say the highest score on the exam was 105, 95 isn't far off and it's seen as an accomplishment to only be
10 off from that. But then you find out that the mean was 100 and their 95 was actually the lowest score. You feel terrible for them!! But.
Literally, 95 is absolutely meaningless unless you are given other additional info to shape and form the situation and
what the number actually means.
So what does the meaning of a score depend on?
The rest of the scores/results
Name three things you can calculate with a raw score that would allow you to gauge its relationship to other scores
Percentiles, z scores, outliers
What is a z score?
It tells us the relationship of an individual score to both the mean and the standard deviation of its fellow scores.
The absolute value of the z score tells the number of standard deviations the score is from the mean.
Is also used to compare two scores from two different distributions, even when the score are measuring different things
What is the formula for a z score?
Z = ( X - X bar) / S
What is ( X - X bar )?
The deviation score
How does the deviation score help us analyze an individual score?
Welp. If the deviation score is 5. We know this is above average. Likewise if it were to be negative we would know that
this would be below average.
From this deviation score of 5, we only know that the score is better than average, but we have no idea how above average
If the distribution had a range of 10 units and X bar = 50, then an X of 55 is a very high score.
On the other hand, if the distribution has a range of 100 units, an X of 55 is barely above average.
How do we find a score's position in a distribution?
You take its variability into account. To do this you have to divide ( X - X bar ) by a unit that measures variability,
A z score is also referred to as a?
What is a standard score?
A score expressed in standard deviation units
What type of data can be converted into z scores?
Any distribution of raw scores, for each raw score there is a z score
If z score is pos/neg?
Positive- raw scores greater than the mean
Neg- raw scores lesser than the mean
If two raw scores are converted into z scores what does this tell us?
the two z scores tell us their positions relative to each other as well as to the distribution
Bro. Just. Look at this table and be able to explain common misconceptions
Table 5.1 on page 74
My mind was so blown when I just learned what it meant by z is measured in standard deviation units.
What is an outlier?
Scores in a distribution that are unusually large or unusually small.
An extreme score separated by others
It has a disproportionate influence, compared to any of the other scores, on the mean, standard deviation, and
other statistical measures
What is a box plot?
It is a way to illustrate a distribution's range, interquartile range, skew, median, and sometimes other statistics.
You get two measures of central tendency, two measures of variability, and a way to estimate skewness.
How does a box plot give you central tendency?
It gives you two.
The median is the vertical line inside the box.
The mean is the dot.
How does a box plot give you variability?
It gives you two.
The box gives you the interquartile range.
The left end of the box is the 25th percentile score, the right end is the 75th percentile score
The whiskers give you a picture of the range, because they extend to the extreme scores in the distribution
How does a box plot give you skewness?
It gives skewness in two different ways.
1. The relationship between the mean and the median and any difference in the lengths of the whiskers.
When the mean is less than the median, the skew is negative
When the mean is greater than the median, the skew is positive
2. Skewness is also indicate by whiskers of different lengths.
The longer the whisker is over the lower scores, the skew is negative
If the longer whisker is over the higher scores, the skew is positive
What is the effect size index?
It is the statician's way of answering the question, how much difference is there?
It is the amount or degree of separation between two distributions
IT IS THE DIFFERENCE BETWEEN MEANS PER STANDARD DEVIATION UNIT
What is the equation for effect size index?
d = (weird u)1 - (weird u)2 / weird o
and for a sample you use X bar and not the weird u
What qualifies as a small, medium, and large effect?
small: d = 0.20
medium: d = 0.50
large: d = 0.80
Write out how you would describe a small, medium, and large effect and what it would look like graphically on a
frequency polygon and boxplot(shown on pg. 81)?
d = 0.20, the mean of distribution B is two-tenths of a standard deviation unit greater than the mean of
distribution A (d = 0.20)
The frequency polygons are HELLA close together, they overlap so much you can barely tell they're different.
The box plots mean/medians are also barely different as well
For a medium, where d = 0.50, mean of distribution B would be five-tenths, or one-half of a standard deviation unit greater
Frequency polygon- you can tell they're different, but they still overlap somewhat
box plot- same as frequency polygon
For a large, where d = 0.8, the frequency polygon look very different and don't even overlap except once where they cross
box plot- mean and averages link at the edges it looks like
What makes a negative/positive effect size index (d value)?
There is no such thing as neg/pos., it's arbitrary