Descriptive Statistics

Describe the features of frequency bar charts, histograms, and polygons. Discuss what kind of data is graphed using each and why.

-A frequency bar chart graphs the counts of nominal data, and a frequency histogram graphs the counts of numerical data. The difference between the two graphs in appearance is that the bars do not touch in the bar chart, but they do touch in the histogram. This is because if you mixed the scores in a different order in a numerical data set, it wouldn't make sense. With the bars touching it conveys that the data cannot be move in a different order. -A frequency polygon is also used to measure numerical data, and it has a line connecting the data points instead of bars, like the histogram. Like the frequency histogram, the frequency histogram is also helpful for numerical data because it keeps the data in the correct order.

In addition to frequencies, describe the two classes of statistics used to assess numerical data. List and define the three examples from each class.

-Central Tendency- the center or middle of the distribution. Three examples of central tendency: mean (average), median (center/50th percentile), mode (most occurring score) -Variability- how spread out the data set is. Three examples of variability: range (highest score-lowest score), variance (SD^2), and standard deviation (average deviation from the mean)

Describe the purposes of descriptive versus inferential statistics.

-Descriptive statistics describe and summarize data sets, while inferential statistics is used to test hypotheses

Describe and give an example of nominal and numerical data.

-Nominal data is a grouping variable or a difference of a kind. An example is gender or political affiliation -Numerical data is a measurement or score or a difference of degree. An example is temperature.

List and describe the three features of a distribution.

1. Central tendency - the center or middle of the distribution 2. variability - the spread or scatter around the mean 3. skew - how balanced or symmetrical the distribution is (normal, positive, negative)

List and describe three statistics used to describe nominal data.

1. frequencies- count, measured by a frequency bar chart 2. proportions- sample/population 3. percentages- proportionx100

Given a z-score be able to convert it into a percentile score.

1. locate the z-score in table and find% undercurve 2. if z-score is positive, add 50% to table value 3. if z-score is negative, subtract table value from 50%

Given a raw score be able to convert it to a z-score and be able to interpret this z-score in words

ex. raw score=13, mean=11, SD=1 z=(13-11)/1=2 Raw score is 2SD above the mean on ____ scale

Describe how the standard deviation is similar to the mean as the "average deviation from the mean." Include, with formulas, the ideas of a score, totaling of scores and averaging of scores. Be sure to include, at each step, the formula for the deviation score, sum of squares and conclude with the full formula for the standard deviation.

mean: x=score Ex=total score x(with - on top)=Ex/N=average scores the three ideas of the mean are used in the standard deviation: Standard deviation: (x-x(with - on top))=score E(x-x(with - on top))^2=total deviation or "sum of squares" SD= square root of (E(x-x(with - on top))^2)/N = average deviation

List the mean and standard deviation of the z-score distribution.

mean: 0 SD: 1

describe positive and negative skew

positive skew: has a tail towards extreme high scores with mode closer to the low score at the highest point of the curve, a mean pulled toward the extreme high scores, and a median between the mode and mean negative skew: has a tail towards extreme low scores with mode closer to the high scores at the highest point of the curve, a mean pulled toward the extreme low scores, and a median between the mode and mean

Describe the metric problem and how z-scores help overcome this problem.

the metric problem is the difficulty in interpreting unknown metrics or comparing or combining different metrics. Z-scores give a standard, common metric by expressing everything in units of standard deviation.

Given a mean and a standard deviation for a distribution, describe the nature of the distribution

using the SD of ______ and the mean of _______, 68% of scores lie between _______ and _______, and 96% of scores lie between ______ and ______

Describe the statistical idea of standardization using the formula for the z-score.

z= (x-x(with - on top))/SD This formula expresses the score's distance from the mean (in the numerator), and it expresses that distance in SD units (in the denominator).