STATISTICS Flashcards
the act of assigning numbers or symbols to characteristics of things according to rules
Measurement
methods used to provide concise description of a collection of quantitative information
Descriptive Statistics
method used to make inferences from observations of a small group of people known as sample to a larger group of individuals known as population
Inferential Statistics
the property of “moreness”
Magnitude
the difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units
Equal Intervals
when nothing of the property being measured exists
Absolute 0
a set of numbers who properties model empirical properties of the objects to which the numbers are assigned
Scale
takes on any value within the range and the possible value within that range is infinite
- used to measure a variable which can theoretically be divided
Continuous Scale
can be counted; has distinct, countable values
- used to measure a variable which cannot be theoretically be divided
Discrete Scale
refers to the collective influence of all the factors on a test score or measurement beyond those specifically measured by the test or measurement
Degree to which the test score/measurement may be wrong, considering other factors like state of the testtaker, venue, test itself etc.
Measurement with continuous scale always involve with error
Error
involve classification or categorization based on one or more distinguishing characteristics
- Label and categorize observations but do not make any quantitative distinctions between observations
- mode
Nominal
rank ordering on some characteristics is also permissible
- median
Ordinal
- contains equal intervals, has no absolute zero point (even negative values have interpretation to it)
- Zero value does not mean it represents non
Interval
- has true zero point (if the score is zero, it means none/null)
- Easiest to manipulate
Ratio
– defined as a set of test scores arrayed for recording or study
Distribution
– straightforward, unmodified accounting of performance that is usually numerical
Raw Scores
– all scores are listed alongside the number of times each score occurred
Frequency Distribution
– being manipulated in the study
Independent Variable
nonmanipulated variable to designate groups
Factor: for ANOVA
Quasi-Independent Variable
– used in ANOVA to determine which mean differences are significantly different
Post-Hoc Tests
allows the compute a single value that determines the minimum difference between treatment means that is necessary for significance
Tukey’s HSD test
statistics that indicates the average or midmost score between the extreme scores in a distribution
Goal: Identify the most typical or representative of entire group
Measures of Central Tendency
– the average of all the raw scores
- Equal to the sum of the observations divided by the number of observations
- Interval and ratio data (when normal distribution)
- Point of least squares
- Balance point for the distribution
Mean
– the middle score of the distribution
- Ordinal, Interval, Ratio
- Useful in cases where relatively few scores fall at the high end of the distribution or relatively few scores fall at the low end of the distribution
- In other words, for extreme scores, use median (skewed)
- Identical for sample and population
- Also used when there has an unknown or undetermined score
- Used in “open-ended” categories (e.g., 5 or more, more than 8, at least 10)
- For ordinal data
Median
– most frequently occurring score in the distribution
Mode
if there are two scores that occur with highest frequency
Not commonly used
- Useful in analyses of qualitative or verbal nature
- For nominal scales, discrete variables
- Value of the mode gives an indication of the shape of the distribution as well as a measure of central tendency
Bimodal Distribution
– an indication how scores in a distribution are scattered or dispersed
Variability
statistics that describe the amount of variation in a distribution
Measures of Variability
– equal to the difference between highest and the lowest score
Provides a quick but gross description of the spread of scores
When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated
Range
dividing points between the four quarters in the distribution
Quartile
refers to an interval
Quarter:
measure of variability equal to the difference between Q3 and Q1
Interquartile Range:
equal to the interquartile range divided by 2
Semi-interquartile Range:
equal to the square root of the average squared deviations about the mean
Equal to the square root of the variance
Standard Deviation –
equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
Distance from the mean
Variance:
– also known as Gaussian Curve
Bell-shaped, smooth, mathematically defined curve that is highest at its center
Normal Curve
_______ = approaches but never touches the axis
Asymptotically
2 – 3 standard deviations above and below the mean
Tail
right side of the graph is mirror image of the left side
Has only one mode and it is in the center of the distribution
Mean = median = mode
Symmetrical Distribution
nature and extent to which symmetry is absent
Skewness
few scores fall the high end of the distribution
The exam is difficult
More items that was easier would have been desirable in order to better discriminate at the lower end of the distribution of test scores
Positive Skewed
when relatively few of the scores fall at the low end of the distribution
The exam is easy
More items of a higher level of difficulty would make it possible to better discriminate between scores at the upper end of the distribution
Negative Skewed
____ is associated with abnormal, perhaps because the skewed distribution deviates from the symmetrical or so-called normal distribution
Skewed
– steepness if a distribution in its center
Kurtosis
relatively flat
Platykurtic
relatively peaked
Leptokurtic
somewhere in the middle
Mesokurtic
high peak and fatter tails
High Kurtosis
rounded peak and thinner tails
Lower Kurtosis
raw score that has been converted from one scale to another scale
Standard Score
– results from the conversion of a raw score into a number indicating how many SD units the raw score is below or above the mean of the distribution
Z-Scores
– a scale with a mean set at 50 and a standard deviation set at 10
T-Scores
a method of scaling test scores on a nine-point standard scale with a mean of five (5) and a standard deviation of two (2)
Stanine
one that retains a direct numerical relationship to the original raw score
Linear Transformation
– required when the data under consideration are not normally distributed
Nonlinear Transformation
Normalizing the distribution involves stretching the skewed curve into the shape of a normal curve and creating a corresponding scale of standard scores, a scale that is technically referred to as _______________
Normalized Standard Score Scale
standard to ten; divides a scale into 10 units
STEN
– statistical method that uses a sample data to evaluate a hypothesis about a population
Hypothesis Testing
– states there is a change, difference, or relationships
Alternative Hypothesis
– no change, no difference, or no relationship
Null Hypothesis
used to define concept of “very unlikely” in a hypothesis test
Alpha Level or Level of Significance
– composed of extreme values that are very unlikely to be obtained if the null hypothesis is true
Critical Region
If sample data fall in the critical region, the null hypothesis is _______
rejected
