Chapter 5- Other Descriptive Statistics

Question 1

Why would someone giving you the statement “I got a 95 on my math exam!” be statistically meaningless to you?

Answer 1

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.

Question 2

So what does the meaning of a score depend on?

Answer 2

The rest of the scores/results

Question 3

Name three things you can calculate with a raw score that would allow you to gauge its relationship to other scores

Answer 3

Percentiles, z scores, outliers

Question 4

What is a z score?

Answer 4

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

Question 5

What is the formula for a z score?

Answer 5

Z = ( X - X bar) / S

Question 6

What is ( X - X bar )?

Answer 6

The deviation score

Question 7

How does the deviation score help us analyze an individual score?

Answer 7

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
it is.
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.

Question 8

How do we find a score’s position in a distribution?

Answer 8

You take its variability into account. To do this you have to divide ( X - X bar ) by a unit that measures variability,
standard deviation.

Question 9

A z score is also referred to as a?

Answer 9

Standard score

Question 10

What is a standard score?

Answer 10

A score expressed in standard deviation units

Question 11

What type of data can be converted into z scores?

Answer 11

Any distribution of raw scores, for each raw score there is a z score

Question 12

If z score is pos/neg?

Answer 12

Positive- raw scores greater than the mean

Neg- raw scores lesser than the mean

Question 13

If two raw scores are converted into z scores what does this tell us?

Answer 13

the two z scores tell us their positions relative to each other as well as to the distribution

Question 14

Bro. Just. Look at this table and be able to explain common misconceptions
Table 5.1 on page 74

Answer 14

My mind was so blown when I just learned what it meant by z is measured in standard deviation units.

LIKE. DANGGGGG

Question 15

What is an outlier?

Answer 15

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

Question 16

What is a box plot?

Answer 16

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.

Question 17

How does a box plot give you central tendency?

Answer 17

It gives you two.
The median is the vertical line inside the box.
The mean is the dot.

Question 18

How does a box plot give you variability?

Answer 18

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

Question 19

How does a box plot give you skewness?

Answer 19

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

Question 20

What is the effect size index?

Answer 20

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

Question 21

What is the equation for effect size index?

Answer 21

d = (weird u)1 - (weird u)2 / weird o

and for a sample you use X bar and not the weird u

Question 22

What qualifies as a small, medium, and large effect?

Answer 22

small: d = 0.20
medium: d = 0.50
large: d = 0.80

Question 23

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)?

Answer 23

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

Question 24

What makes a negative/positive effect size index (d value)?

Answer 24

There is no such thing as neg/pos., it’s arbitrary

Question 25

How would you find the interquartile range of a box plot?

Answer 25

It is the distance between the mean and the median. So the distance between the dot and the line.