Statistics Alive! Flashcards
Kurtosis
Height of a distribution is affected by too many or too few middle scores
Leptokurtic
A distribution with many middle scores
Platykurtic
A distribution with few middle scores
Nominal scale
Classifies cases into categories
Ordinal scale
Ranks scores by degree to which they possess the measured trait
Interval scale
Distances between adjacent scores are equal and consistent throughout the scale. (equal-interval scale)
Ratio scale
Interval scale with addition of absolute zero point.
Continuos variable
Variables where values could theoretically fall between adjacent scale units (height, weight, time)
Discrete data
Values that cannot theoretically fall between adjacent scale units (people, photos, etc)
Real limit
Half the scale’s unit (real limit opposed to observed scores)
Frequency table
Lists each observed score along with number of cases falling at each score
Cumulative frequency table
Shows how many scores are at or below (or at or above) any given score
Relative frequency or percentage table
Gives each score’s frequency relative to 100% (values will all be between 0-100).
Cumulative relative frequency or cumulative percentage table
Shows percentage above or below a given score
Grouped frequency table
Frequency table with score intervals. Can show patterns but have to get right size intervals (not too big or small) by guess and check.
Percentile rank table
Indicates percentage of cases falling at or below a given score (not below a given score)
Percentile
The score falling at a particular percentile rank (can be any score on table while percentages will be between 0-100)
Stem-and-leaf display
Hybrid between table and graph with left column indicating first digit of a score and right column indicating every instance of the next digit
Abscissa
X-axis
X-axis
Abscissa
Ordinate
Y-axis
Y-axis
Ordinate
Frequency curve or line graph
Midpoints of data connected by a line without bars
Skewed
Asymmetric distribution with a single peak
Negatively skewed
Many high scores
Positively skewed
Many low scores
Bimodal
A distribution with 2 peaks. Usually an indication that sample contains two distinct subgroups.
Rectangular distribution
Uniform score distribution (like graphing ranks if there are no tied ranks)
Bar graph
Graph appropriate for nominal data with x-axis reflecting categories instead of scores
Pie graph
Circle graph with slices representing percentages
Inflection points
Changes in the curve direction of a graphical distribution.
Normal curve
Symmetric bell-shaped curve having inflection points at exactly 1 standard deviation above and 1 standard deviation below the mean. At the points indicated, steepness of the curve changes from steeply down to gently out.
In a normal curve the mean, media , and mode…
All fall at the same point
Asymptotic
Curve never reaches x-axis allowing for scores in tails of distribution.
Limits to normal curve
Only a theoretical distribution. How scores would distribute if infinite scores were collected. The smaller the sample size, the greater the deviation from percentages associated with normal curve.
Normal curve is robust to minor violations of its shape assumptions
We can use the percentages associated with the normal curve to interpret data even when our data are only approximately normally distributed.
Dispersion
Measures of spread or variability within a set of scores
Central tendency
Summarize in a single value the centrality of the data
Mode
Most frequent score
Mo
Mode
Limits to mode
Least stable of 3 measures of central tendency. No additional statistics are based on mode.
Median
Middle score
Mdn
Median
Mean
Average score
M
Mean for samples
m (mew)
Mean for populations
Limits to mean
Most sensitive to score aberrations/outliers
Outlier
Score that is way out of line with rest of the data
What happens to median, mean, and mode in skewed data?
Mode remains stable, mean pulled toward tail, median falls between mean and mode.
If mean is lower than mode, distribution is…
Negatively skewed
If mean is higher than mode…
Distribution is positively skewed
Report the mean unless…
- There are unknown values. 2. The distribution is seriously skewed 3. Distribution is bimodal or multimodal
Report what measure of central tendency for multimodal distributions?
1 mode for each sub-group (2 modes for bimodal)
Range
Difference between the lowest and highest scores in a data set.
Limits to range
Subject to vagaries of cases that happen to fall at either end of a particular sample. No other statistics are based on range.
Variance
Average area distance from the mean (average of squared deviation scores).
Deviation score
Amount by which a raw score deviates from the mean
Standard deviation
Average linear distance from the mean. Square root of the variance.
Average absolute deviation
Take absolute value of each deviation rather than squaring. Then sum and average. (compare to variance/SD). Does not fall in known locations on normal curve and infrequently used.
Standard score
Score expressed in standardized unit of measurement in interval measure. Tells value of a score relative to all other scores (and central tendency and dispersion scores)
Z score
Raw score re-expressed in standard deviation units. The number of standard deviation units that a score is above or below the mean
Rescale
Change the scale of data to covert to different measurement
Z score accounts for…(3 things)
Central tendency (M), dispersion (s), and sample size (N)
What score allows for comparison across differing tests?
Z score
Transformation
An adjustment applied equally to all scores in a set
Effect on the mean of adding or subtracting a constant from every score
Mean goes up or down by same amount
Effect oh mean of multiplying or dividing every score by a constant
Mean is multiplied or divided by same amount
Effect on standard deviation of adding or subtracting a constant from every score
Standard deviation stays the sams
Effect on standard deviation of multiplying or dividing every score by a constant
Standard deviation is multiplied or divided by same amount
Probability
Relative frequency of a particular outcome occurring over an infinite number of trials or occasions. Expressed as a proportion from .00 to 1.00
Equally likely model
Generating event yields possible outcomes that are equally likely (e.g coin tossing)
Mutually exclusive outcome
Outcome of a particular trial precludes any other outcome for that same trial (as opposed to embedded [college student and sophomore] or overlapping [college student and employee] outcomes)
When does the addition theorem apply?
When outcomes are mutually exclusive
Addition theorem
The probability of any of the possible outcomes occurring on a particular trial is the sum of their individual probabilities
Ideoendent outcome
Outcome of one trial had no relation to the outcome of another trial. Always refers to series of trials.