STATISTICAL FOUNDATIONS Flashcards by Ariel IPAD

involves the use of certain devices or rules for assigning numbers to objects or events (Stevens, 1946).

Measurement

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anything that varies and can be classified in a multitude of ways

Variables

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Variables

Types of Variables

Discrete Variables
Continuous Variables
Polytomous Variables
Dichotomous Variables

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Types of Variables

are those with a finite range of values—or a potentially infinite, but countable, range of values.

Discrete variables

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Types of Variables

are discrete variables that can assume only two values, such as sex or the outcome of coin tosses.

Dichotomous variables

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Types of Variables

are discrete variables that can assume more than two values, such as marital status, race, and so on.

Polytomous variables

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Types of Variables

such as time, distance, and temperature, on the other hand, have infinite ranges and really cannot be counted.

Continuous variables

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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)

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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)

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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)

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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)

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A. Scales of Measurement

Properties of Scales

Magnitude
Equal Intervals
Absolute 0

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Properties of Scales

is the property of “moreness.”

Magnitude

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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

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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

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Properties of Scales

__ is obtained when nothing of the property being measured exists.

Absolute 0

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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)

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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)

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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)

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A. Scales of Measurement

Types of Scales

Nominal Scale
Ordinal Scale
Interval Scale
Ratio Scale

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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

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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

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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

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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

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# 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

- 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 ## Footnote 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