Statistics in Psychology - Chapter II

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Questions and Answers

What are the two main purposes of statistics?

Description and inference

What does 'magnitude' refer to in a scale of measurement?

Moreness

Which type of scale has the properties of magnitude, equal intervals, and an absolute zero?

  • Ordinal
  • Interval
  • Ratio (correct)
  • Nominal

A histogram is a type of graph that uses bars to represent the frequencies of categorical data.

<p>False (B)</p> Signup and view all the answers

What is the difference between the mean and the median?

<p>The mean is the average of all scores, whereas the median is the middle score in a distribution.</p> Signup and view all the answers

What is the purpose of a standard deviation?

<p>It is a measure of variability that describes the spread of scores around the mean.</p> Signup and view all the answers

A positively skewed distribution has a tail extending to the right of the distribution.

<p>True (A)</p> Signup and view all the answers

What is the difference between a norm-referenced test and a criterion-referenced test?

<p>A norm-referenced test compares an individual's score to a norm group, whereas a criterion-referenced test measures an individual's mastery of specific skills or knowledge.</p> Signup and view all the answers

What is a scatterplot used for?

<p>To visually represent the relationship between two variables.</p> Signup and view all the answers

Flashcards

Scales

A set of numbers whose properties model the empirical qualities of the objects they are assigned.

Magnitude

The property of "moreness." A particular instance of the attribute represents more, less, or equal amounts of the given quantity than does another instance.

Equal Intervals

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.

Absolute Zero

Obtained when nothing of the property being measured exists.

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Nominal Scale

A scale that only names or categorizes objects.

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Ordinal Scale

A scale that ranks objects according to magnitude but doesn't have equal intervals or an absolute zero.

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Interval Scale

A scale that has both magnitude and equal intervals but not an absolute zero.

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Ratio Scale

A scale that has magnitude, equal intervals, and an absolute zero.

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Raw Score

The raw, unmodified score of a test.

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Frequency Distribution

A visualization that shows how frequently each score occurs in a dataset.

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Histogram

A type of graph used for continuous data. It uses vertical bars to represent the frequency of each score.

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Bar Graph

A type of graph used for categorical data. It uses bars to represent the frequency of each category.

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Frequency Polygon

A type of graph used for continuous data. It uses a continuous line to connect points representing the frequency of each score.

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Percentile Rank

The percentage of scores that fall below a specific score.

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Percentile

A specific score or point within a distribution that divides the total frequency into hundredths.

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Measures of Central Tendency

A statistic that represents the central or average score in a distribution.

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Mean

The most commonly used measure of central tendency for interval and ratio data. It is the arithmetic average of all scores.

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Median

The middle score in a distribution, especially useful when the distribution has outliers.

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Mode

The most frequently occurring score in a distribution.

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Variability

An indication of how spread out or dispersed the scores are in a distribution.

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Range

The difference between the highest and lowest scores in a distribution.

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Interquartile Range

The difference between the 75th percentile (Q3) and the 25th percentile (Q1).

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Standard Deviation

A measure of variability equal to the square root of the average squared deviations from the mean.

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Variance

A measure of variability equal to the square root of the variance.

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Skewness

A measure of the symmetry or asymmetry of a distribution. It indicates if the distribution is skewed to one side.

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Kurtosis

A measure of the peakedness or flatness of a distribution.

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Norms

The performance of a defined group on a particular test. It provides information about performance relative to a standardization sample.

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Normal Curve

A bell-shaped, smooth, mathematically defined curve that is highest at its center. The mean, median, and mode are all equal.

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Normal Distribution

A distribution of scores that follows the shape of a normal curve.

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Standard Score

A raw score that has been converted from one scale to another scale with a set mean and standard deviation.

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Z-Score

A standard score with a mean of 0 and a standard deviation of 1. It is the difference between a raw score and the mean divided by the standard deviation.

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T-Score

A standard score with a mean of 50 and a standard deviation of 10. It is a type of standard score that eliminates negative scores.

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Stanine

A standard score with a mean of 5 and a standard deviation of 2. It is a type of standard score that is used to summarize the scores of a large number of test takers.

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STEN

A standard score with a mean of 5.5 and a standard deviation of 2. It is a type of standard score that is similar to the Stanine.

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Correlation Coefficient

The strength of the relationship between two variables. It tells us the direction of the relationship (positive or negative) and how strong the relationship is.

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Pearson Correlation Coefficient

A statistical test used to determine the strength of the linear relationship between two continuous variables.

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Spearman's Rho

A statistical test used to determine the strength of the relationship between two ranked variables.

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Point-Biserial Correlation

A statistical test used to determine the strength of the relationship between one dichotomous variable and one continuous variable.

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Phi-Coefficient

A statistical test used to determine the strength of the relationship between two dichotomous variables.

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Study Notes

Chapter II: Introduction

  • Statistics transforms data into information and practice, crucial for an information-based society.
  • Understanding basic statistics is essential to avoid manipulation and ensure informed decision-making.
  • Statistics is a critical mathematical discipline for processing data into meaningful information.
  • Basic statistical knowledge empowers individuals to interpret data encountered in everyday life.
  • Psychological conclusions about human behavior need statistical methods to derive valid conclusions.
  • Data collection requires sampling from populations to minimize bias.
  • Rigorous statistical analysis supports hypothesis testing.
  • This chapter provides a refresher course on statistics and its use in psychological assessment.

Lesson Proper: Why Statistics?

  • Statistics concisely describes observations, comparing them to one another.
  • Logical conclusions about unobserved events can be drawn using statistics.
  • Descriptive statistics describes data in a concise form
  • Inferential statistics uses data from a segment to draw conclusions about a larger group

Measurement: Scales

  • Scales assign numbers to characteristics following rules.
  • Continuous scales measure continuous variables.
  • Discrete scales categorize variables without numerical meaning.
  • Scale properties include magnitude (more/less), equal intervals (same meaning using scale units), and absolute zero (absence of the characteristic.)
  • Examples of psychological tests (IQ levels) rarely exhibit equal intervals or absolute zero points.

Types of Measurement Scales

  • Nominal scale: categorizes objects.
  • Ordinal scale: ranks objects but does not define differences between ranks.
  • Interval scale: ranks objects with equal interval sizes but no absolute zero.
  • Ratio scale: ranks objects with equal interval sizes and an absolute zero point.

Describing Data: Frequency Distributions & Graphic Forms

  • Frequency distributions: show how often each score occurs.
  • Graphic forms: represent data visually with Histograms, Bar Graphs, and Frequency Polygons.

Measures of Central Tendency

  • Mean: The average score.
  • Median: The middle score in a distribution.
  • Mode: The most frequent score.
  • Mean is the most commonly used measure for interval/ratio data.
  • Median is more useful when few extreme scores exist in a data set.
  • Mode is appropriate for nominal data though isn't very common

Measures of Variability

  • Standard Deviation and Variance calculate data spread.
  • Skewness measures symmetry.
  • Kurtosis measures the peakedness.
  • Range, Interquartile Range are also used to measure variablity.

Normal Curve

  • The normal curve displays a bell-shaped distribution.
  • Mean, median, and mode are all located at the peak.
  • Standard deviation units measure distance from mean in either direction.
  • A well-established theory describes the distribution patterns under ideal conditions and is useful for inferential testing.

Correlation

  • Correlation measures the relationships between variables.
  • Correlation coefficients (e.g., Pearson r, Spearman ρ) quantify the strength and direction of these relationships.
  • A correlation does not imply causation. (Correlation does not equal causation).
  • Positive, negative, and no correlation are indicative of the relationship between two variables.

Tests of Correlation

  • Pearson r is commonly used to examine linear relationships between continuous variables.
  • Spearman ρ measures the relationship between ranked data.
  • Point-biserial correlation measures association when one variable is dichotomous (e.g., yes/no) and the other is continuous.
  • Phi coefficient is used for two dichotomous variables.

Regression

  • Regression is a procedure for predicting scores on one variable from scores on another.
  • Multiple regression uses more than one predictor variable.

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