STATISTICAL FOUNDATIONS Flashcards
involves the use of certain devices or rules for assigning numbers to objects or events (Stevens, 1946).
Measurement
anything that varies and can be classified in a multitude of ways
Variables
Variables
Types of Variables
- Discrete Variables
- Continuous Variables
- Polytomous Variables
- Dichotomous Variables
Types of Variables
are those with a finite range of values—or a potentially infinite, but countable, range of values.
Discrete variables
Types of Variables
are discrete variables that can assume only two values, such as sex or the outcome of coin tosses.
Dichotomous variables
Types of Variables
are discrete variables that can assume more than two values, such as marital status, race, and so on.
Polytomous variables
Types of Variables
such as time, distance, and temperature, on the other hand, have infinite ranges and really cannot be counted.
Continuous variables
Types of Variables
A researcher is studying the number of children in different households. What type of variable is this?
Discrete Variable
(because the number of children is countable and finite)
Types of Variables
A hospital records whether patients test positive or negative for a disease. What type of variable is this?
Dichotomous Variable
(since it has only two possible values)
Types of Variables
A researcher classifies people based on their blood type (A, B, AB, O). What type of variable is this?
Polytomous Variable
(because it has more than two possible values)
Types of Variables
A stopwatch is used to measure the time it takes for a runner to finish a race. What type of variable is this?
Continuous Variable
(because time can take any value within an infinite range)
A. Scales of Measurement
Properties of Scales
- Magnitude
- Equal Intervals
- Absolute 0
Properties of Scales
is the property of “moreness.”
Magnitude
Properties of Scales
A scale has the property of __ if we can say that a particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance
Magnitude
Properties of Scales
A scale has the property of __ if 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
Properties of Scales
__ is obtained when nothing of the property being measured exists.
Absolute 0
Properties of Scales
In a race, if we rank runners as 1st, 2nd, and 3rd based on their finishing times, which property of measurement does this represent?
Magnitude
(because rankings show relative “moreness” in terms of speed)
Properties of Scales
On a thermometer, the difference between 10°C and 20°C is the same as the difference between 30°C and 40°C. Which property does this illustrate?
Equal Intervals
(since the difference between units remains constant across the scale)
Properties of Scales
If a scientist measures the number of bacteria in a sample and gets a count of 0, meaning there are no bacteria present, which property is being shown?
Absolute Zero
(because the absence of bacteria is a true zero)
A. Scales of Measurement
Types of Scales
- Nominal Scale
- Ordinal Scale
- Interval Scale
- Ratio Scale
Types of Scales
Scales, numbers are used solely as labels to identify an individual or a class. It is used when the information is qualitative
Nominal Scale
Types of Scales
there is the property of rank order, which means that the elements in a set can be lined up in a series—from lowest to highest or vice versa—arranged on the basis of a single variable
Ordinal Scale
Types of Scales
also known as equal-unit scales, the difference between any two consecutive numbers reflects an equal empirical or demonstrable difference between the objects or events that the numbers represent.
Interval Scale
Types of Scales
the use of this type of measurement scale is common; times, distances, weights, and volumes can be expressed as ratios in a meaningful and logically consistent way.
Ratio Scale
Types of Scales
A scale that has all three properties (magnitude, equal intervals, and an absolute 0)
Ratio Scale
Types of Scales
A student’s ID number is used only for identification purposes and does not indicate rank or order. What type of scale is this?
Nominal Scale
Types of Scales
In a marathon race, runners are ranked 1st, 2nd, and 3rd based on who finishes first. What type of scale does this represent?
Ordinal Scale
Types of Scales
A thermometer shows a temperature of 20°C, and another thermometer shows 30°C. The difference between them is the same as between 50°C and 60°C.
Interval Scale
Types of Scales
A weighing scale shows that one bag weighs 5 kg and another weighs 10 kg. Since 10 kg is twice as heavy as 5 kg, what type of scale is being used?
Ratio Scale
What type of statistics is used to provide a concise description of a collection of quantitative information?
Descriptive Statistics
What type of statistics is used to make conclusions from a sample to a larger population?
Inferential Statistics
What do we call a set of test scores arranged for recording or study?
Distribution
What is a straightforward, unmodified numerical accounting of performance?
Raw Score
What method displays scores on a variable along with the number of times each score occurred?
Frequency Distribution
What statistical measure answers the question, “What percent of the scores fall below a particular score?”
Percentile Rank
What do we call specific points within a distribution that divide the total frequency into hundredths?
Percentile
What type of statistics is used when data from a sample is used to estimate population values or test hypotheses?
Inferential Statistics
What statistical measure helps adjust for the number of scores in a group instead of simply ranking them?
Percentile Rank
What type of statistics includes numbers and graphs used to describe, condense, or represent data?
Descriptive Statistics
indicates the average or midmost score between the extreme scores in a distribution.
Measures of Central Tendency
Measures of Central Tendency
- Mean
- Median
- Mode
Measures of Central Tendency
The arithmetic average score in a distribution.
Mean
Measures of Central Tendency
The middle score in a distribution, is another commonly used measure of central tendency.
Median
We determine the median of a distribution of scores by ordering the scores in a list by magnitude, in either ascending or descending order.
Measures of Central Tendency
The most frequently occurring score in a distribution of scores
Mode
Measures of Central Tendency
Two scores that occur with the highest frequency.
Bimodal Distribution
Measure of Variability
- Range
- Interquartile and Semi-Interquartile
- Standard Deviation
- Variance
- Skewness
- Kurtosis
Measure of Variability
The difference between the highest and the lowest scores
Range
Measure of Variability - Interquartile and Semi-Interquartile
The dividing points between the four quarters in the distribution.
Quarter
Measure of Variability - Interquartile and Semi-Interquartile
Refers to a specific point whereas quarter refers to an interval
Quartile
Measure of Variability - Interquartile and Semi-Interquartile
The difference between Q3 and Q 1.
Interquartile range
Measure of Variability - Interquartile and Semi-Interquartile
The interquartile range divided by 2.
Semi-interquartile range
Measure of Variability
A measure of variability equal to the square root of the average squared deviations about the mean. It is equal to the square root of the variance.
Standard Deviation
Measure of Variability
Is equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean.
Variance
Measure of Variability
The nature and extent to which symmetry is absent
Skewness
Skewness
Relatively few of the scores fall at the high end of the distribution. An indication that the test was too difficult
(The Peak is skewed to the Left)
Positively skewed
Skewness
Relatively few of the scores fall at the low end of the distribution. An indication that the test was too easy.
(The Peak is skewed to the Right)
Negatively Skewed
Measure of Variability
The steepness of a distribution in its center.
Kurtosis
Kurtosis
Types of Kurtosis
- Platykurtic
- Leptokurtic
- Mesokurtic
Kurtosis
The steepness of a distribution in its center is relatively flat.
Platykurtic
Kurtosis
The steepness of a distribution in its center is relatively peaked.
Leptokurtic
Kurtosis
The steepness of a distribution in its center is somewhere in the middle.
Mesokurtic
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 standard deviation units the raw score is below or above the mean of the distribution.
Z scores
A fifty plus or minus ten scale; that is, 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 scale (1-9), with 5 being the average, and is used to compare student performance relative to a group. (Standard Deviation of approxiamately 2)
Stanine
short for “Standard Nine”
The resulting distribution has a mean of 500 and a standard deviation of 100
A scores
Typically has a mean set at 100 and a standard deviation set at 15.
IQ scores
Bell-shaped, smooth, mathematically defined curve that is highest at its center.
NORMAL CURVE
An expression of the degree and direction of correspondence between two things.
CORRELATION
CORRELATION
The most widely used to measure correlation.
The Pearson R
CORRELATION
Rank-order correlation coefficient, a rank difference correlation coefficient
The Spearman Rho
CORRELATION
are visual tools used to show the relationship between two variables.
Graphic Representations of Correlation
CORRELATION
Types of Graphic Representations of Correlation
- Bivariate Distribution
- Scatter Diagram
Types of Graphic Representations of Correlation:
This refers to the distribution of two variables and how they are related to each other.
Bivariate Distribution
Types of Graphic Representations of Correlation:
is a type of graph used to display the relationship between two numerical variables.
Scatter Diagram
CORRELATION
The analysis of relationships among variables for the purpose of understanding how one variable may predict another.
Regression
determining whether correlation is caused by mere chance.
TESTING FOR SIGNIFICANCE
TESTING FOR SIGNIFICANCE
What hypothesis states that there is no correlation between two variables?
Null Hypothesis
(H₀): r = 0
TESTING FOR SIGNIFICANCE
Which hypothesis suggests that a correlation exists between two variables but does not specify the direction?
Alternative Hypothesis
(H₁): r ≠ 0
TESTING FOR SIGNIFICANCE
The probability that a statistical inference is caused pure chance is called the __
P-Value
TESTING FOR SIGNIFICANCE
The maximum level of risk that we are willing to take that our inference is incorrect.
Significance Level
(α) (commonly 0.05 or 5%)
TESTING FOR SIGNIFICANCE
if the correlations involve variables measured using interval scales
Pearson product moment correlations
TESTING FOR SIGNIFICANCE
A table that describes the frequency or percentage of all combinations of two or more nominal or categorical variables
Cross tabulation or contingency table
TESTING FOR SIGNIFICANCE
the average difference between observed and expected counts across all cells
Chi-square
