Study Sheet for Exam 1
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Study Sheet for Exam 1
BESC 3010: Statistics for the Behavioral Sciences
Barton Poulson
Exam 1 covers chapters 01-05. These are the topics that you should pay special attention to.
You can get to the textbook by clicking here.
Chapter 01: Introduction to Statistics
● Levels of measurement
○ How each level differs
○ Which contains the most/least information
○ Examples of each
○ Nominal, ordinal, interval, and ratio
○ Categorical and quantitative
○ Discrete and continuous
○ Coding for nominal variables
● Samples and populations
● Experiments and manipulations
○ Independent and dependent variables
Chapter 02: Distributions
● Calculate frequencies in a data set
● Bar charts, histograms, and boxplots
● Charts that are appropriate for each level of measurement
○ Minimum level of measurement for a bar chart, boxplot, or histogram
● Unimodal and bimodal distributions
● Positive and negative skew
● Kurtosis: platykurtic, mesokurtic, and leptokurtic
○ Values of kurtosis for each shape (e.g., K < 0, K = 0, K > 0)
○ Values for a normal distribution
● Outliers
● Bell curve
Chapter 03: Central Tendency
Study Sheet for Exam 1
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● Mode, median, and mean
○ Calculate each for a data set
● Minimum levels of measurement needed for each measure
● How each is affected by skewness and outliers
○ When each measure works best
● Which measures will be highest or lowest in a skewed distribution
Formulas for Chapter 03
● 𝜇, the population mean:
𝜇
=
𝛴𝑋
𝑁
● 𝑋 = M = the sample mean:
𝛴𝑋
𝑋= 𝑀=
𝑛
Chapter 04: Variability
● How to calculate the range for a data set
○ Uses of the range
● How to calculate the IQR (interquartile range) for a data set
● How to calculate the variance and standard deviation for populations and samples
● Why samples have different formulas that population
● Degrees of freedom
● Deviation values (or deviation scores)
● Sensitivity of each measure to outliers
● Effects of open-ended and undefined scores
● What it means when variability statistics are high vs. when they are low
● Kurtosis: platykurtic, mesokurtic, and leptokurtic (this was also in chapter 02)
○ Values of kurtosis for each shape (e.g., K < 0, K = 0, K > 0)
Formulas for Chapter 04
● The range (same for population and sample):
Range = Xmax – Xmin
Range = Q4 – Q0
● The IQR (same for population and sample):
IQR = Q3 – Q1
Study Sheet for Exam 1
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● Degrees of freedom (for the sample variance and standard deviation):
df = n - 1
● The population variance:
2
𝜎
𝛴(𝑋 − 𝜇)2
=
𝑁
● The population standard deviation:
𝛴(𝑋 − 𝜇)
𝜎 = √𝜎2 = √
2
𝑁
● The sample variance:
2
𝛴(𝑋 − 𝑋)
2
𝑠 =
𝑛−1
● The sample standard deviation:
2
𝛴(𝑋 − 𝑋)
√
2
√
𝑠= 𝑠 =
𝑛−1
Chapter 05: z-Scores
● How to calculate a z-score (i.e., a standardized score) for an individual raw score (i.e.,
an X score)
● Effects of converting an entire distribution of raw scores to z-scores
○ Shape of distribution
○ M and SD of distribution
● What a z-score means
● Percentages of the normal distribution within 1 and 2 standard deviations of the
mean
● Converting X scores (i.e., raw scores) to z-scores
● Converting z-scores to X scores
● Mean, SD, skewness, and kurtosis for normal distributions and/or standardized
distributions
Study Sheet for Exam 1
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○ Note: some of these have only one value; others require additional
information
Formulas
● Calculating a z-score from an X score in a population:
𝑋−𝜇
𝑧=
𝜎
● Calculating a z-score from an X score in a sample:
𝑧=
𝑋−𝑋 𝑋−𝑀
=
𝑠
𝑆𝐷
● Calculating an X score from a z-score for a population:
𝑋 =𝑧∗𝜎+𝜇
● Calculating an X score from a z-score for a sample:
𝑋 =𝑧∗𝑠+𝑋
or, using the preferred APA symbols:
𝑋 = 𝑧 ∗ 𝑆𝐷 + 𝑀
● Proportions of the normal distribution: