Ch 2 Basic Assessment & Statistical Concepts Flashcards
Statistics is: (formal definition)
a set of tools and techniques used for describing, organizing, and interpreting information
Three purposes of statistics:
describe and display data
explain relationships
make conclusions and inferences based on collected data
Statistics are grouped into two categories:
- Descriptive: used to organize and describe the characteristics of a set of data (what, how often, to whom)
- Inferential: used to draw inferences from a small group of data (sample) that can be applied to a larger group (population) (correlations, mean comparisons, hyphothesis testing
statistics is: (informal, Boccone)
a language used to look at and understand data
Variable (definition):
any construct that can assume multiple values
two types of variables:
- Numeric values - quantitative variables
2. Categories - qualitative variables (can be numeric ranges)
Discrete data:
units of measurement that cannot be divided or broken down into smaller units (i.e. # of children you have)
Continuous data
can be subdivided infinitely as they are more approximations based on available data (time - milliseconds, nanoseconds…)
latent variables:
cannot be directly measured, but inferred from the presences of other variables or self-reported by client
Measurement involves:
the application of a specific set of procedures to assign quantitative values (numbers) to various objects, traits, behaviors
Four Scales of Measurement:
- Nominal
- Ordinal
- Interval
- Ratio
four measurement scale properties (each scale is identified by the presence or absence of a set of properties)
- Identification
- Magnitude
- Equal Intervals
- Absolute zero point
Identification =
Each value on the measurement scale has a unique meaning
Magnitude =
Values on the measurement scale have an ordered relationship to one another
Equal intervals =
An equal number of scale units exist between each value along the measurement scale
Absolute zero point =
The measurement scale has a true absolute zero point below which no values exist
Nominal scale of measurement definition and scale property:
used to classify or categorize data into groups that have different names but are not related (ie, names, political parties) - can only name or identify the object being measured
Property = identification
Value of nominal data:
its ability to provide us with percentages and frequencies of scores or clients who may fall into particular categories
Ordinal scale of measurement definition and scale properties:
variables are rank ordered along continuum so each value has a unique meaning and appears in an ordered relationship to other values (ie, 1st, 2nd, 3rd place…)
Properties = identification, magnitude
Interval scale of measurement definition and scale properties:
includes equal intervals which allows definitive statements about an individual’s position on a continuum as well as the positioning relative to others. (ie - IQ scores)
Properties of identification, magnitude and equal intervals. - can add/subtract, but not multiply and create percentages)
Ratio scale of measurement definition and scale properties:
For variables measured on a ratio scale, the value of zero represents the absence of the variable being measured and can do all types of mathematical calculations. (ie - weight, can be weightless, but not negative weight)
Properties - identification, magnitude, equal intervals, absolute zero point
Frequency distribution =
orders a set of disorganized raw scores and summarizes the number of times each of the different scores occurs within a sample of scores
Frequency distribution helps
condense a large set of data into a more manageable display
Simple frequency distribution table =
presents data in two columns: individual scores and # of times score occurred
Mathematical operations done with frequency distribution:
of individuals or scores
proportions
percentages
Two shapes of frequency distributions:
Symmetrical = curve is a mirror image of the other, majority of scores clustered in center of the distribution close to the mean
Asymmetrical = scores are skewed or distorted to one side of the distribution
Asymmetrical scores are skewed in what two ways
positively skewed = majority of scores fall on low end of the distribution
negatively skewed = majority of scores fall on the high end of the distribution
the tail tells the tale
Central tendency =
statistical measure that indicates the center or middle of the distribution
What does central tendency allow for?
Comparisons between groups and individuals
Three measures of central tendency?
Mean
Median
Mode
-work best used together for a full picture
arithmetic Mean =
sum of all scores divided by the total number of scores - the average or mean; don’t use with extreme outliers
Median =
the middle score or the score that divides the distribution exactly in half
(equivalent to the 50th percentile)
Mode =
score that has the greatest frequency in a distribution
Variability =
quantitative measure that describes how spread out or clustered together scores are in a distribution
measures of variability =
statistics that describe the amount of variation in a distribution
three measures of variability =
range
standard deviation
variance
Range =
difference between the highest and lowest value in a distribution
-used with interval and ratio data
standard deviation =
average of amount by which scores vary from the mean
ie - IQ test - standard deviation is 15 in either direction
variance =
the mean of the squared deviation scores (used for computational purposes
standard scores =
indicate the distance an individual’s raw score is above or below the mean of the reference group in terms of standard deviation units
- tells us how many standard deviations a score is away from the mean
standard scores allow for what to be made?
comparisons because the score describe how many SDs an individual’s score is from the mean of that particular distribution
4 types of standard scores =
z-scores t-scores stanines percentiles - all tell us the same thing but in different ways
z-score properties =
mean = 0, SD = 1
most common standard score
How do you obtain a z-score?
convert a raw score into a number that represents how many SDs the raw score is above or below the mean
+ sign indicates SD is above the mean
- sign indicates SD is below the mean
doesn’t tell if a score is good or bad
iq test example - +1 SD means 1 SD above the mean or 115
t-scores properties
mean = 50, SD = 10
How to obtain a t-score?
multiply the z-score by 10 then add 50
stanines
converts raw scores into one of nine possible scores
- rarely used by same concept - how far something is away from the mean
Percentiles =
indicates percentage of people in a reference group that fall at or below the individual’s raw score
- where you fall in relation to the whole group:
50th percentile = you did better than 50%
