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Summary Statistics for the behavioral Sciences (Introduction to statistical analysis CM1005)

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Summary of the book Statistical for the Behavioral Sciences from Privitera (second edition). Suitable for IBCOM and Premaster students at EUR for the course Introduction to statistical analysis CM1005

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  • 20 december 2019
  • 33
  • 2019/2020
  • Samenvatting
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SUMMARY STATISTICS FOR THE
BEHAVIORAL SCIENCES
Gregory J. Privitera
Second edition
Year: 2019/2020
CM1005

,Table of contents
Chapter 1: Introduction to statistics............................................................................................................... 3

Chapter 3: Summarizing data: central tendency.............................................................................................5

Chapter 4: Summarizing data: variability........................................................................................................ 8

Chapter 6: Probability, normal distributions, and Z scores............................................................................13

Chapter 7: Probability and sampling distributions........................................................................................15

Chapter 8: Hypothesis testing: significance, effect size, and power...............................................................18

Chapter 9: Testing means: one-sample and two-independent-sample t tests................................................21

Chapter 11: Estimation and confidence intervals..........................................................................................23

Chapter 12: Analysis of variance: one way between subjects design.............................................................25

Chapter 15: Correlation................................................................................................................................ 29

Chapter 16: Linear regression and multiple regression..................................................................................31

Chapter 17: nonparametric tests: chi-square tests........................................................................................32

,Chapter 1: Introduction to statistics
Statistics = a branch of mathematics used to summarize, analyze, and interpret what
we observe – to make sense or meaning of our observations. Really, statistics is used to
make sense of the observations we make.

Descriptive statistics = procedures used to summarize, organize and make sense of a
set of scores or observations. Descriptive statistics are typically presented graphically, in
tabular form or as summary statistics. Are typically used to quantify the behaviors
researchers measure.

Inferential statistics = procedures used to allow researchers to infer or generalize
observations made with samples to the larger population from which they were selected.

Descriptive statistics  applying statistics to organize and summarize information
Inferential statistics  applying statistics to interpret the meaning of information

Data = the recorded observations that researchers make.

General structure for making scientific observations
1. Ask a question
2. Set up a research study
3. Evaluate findings
4. Measure behavior

Mean = average
Median = middle
Mode = common

Tables and graphs serve a similar purpose to summarize large and small sets of data.
One particular advantage of tables and graphs is that they can clarify findings in a
research study.

Population = the set of all individuals items, or data of interest. This is the group about
which scientists will generalize

Population parameter = a characteristic (usually numeric) that describes a population

Sample = a set of individuals, items, or data selected from a population of interest

Sample statistic = a characteristic (usually numeric) that describes a sample. This is
the value that is measured in the study. A sample statistic is measured to estimate the
population parameter.

1.4 Scales of measurement
in all, scales of measurement are characterized by 3 properties:
1. Order: does a larger number indicate a greater value than a smaller number?
2. Difference: does subtracting two numbers represent some meaningful value?
3. Ratio: does dividing two
numbers represent some
meaningful value?



Scales of measurement = rules
for how the properties of numbers
can change with different uses

, - Nominal scales: measurements in which a number is assigned to represent
something or someone
- Ordinal scales: measurements that convey order or rank alone
- Interval scales: measurements that have no true zero and are distributed in equal
units
- Ratio scales: measurements that have a true zero and are distributed in equal
units

Coding = the procedure of converting a nominal or categorical variable to a numeric
value

true zero = when the value 0 truly indicates nothing on a scale of measurement.
Interval scales do not have a true zero

researchers also distinguish between the types of data they measure. The variables for
which researchers measure data fall into two broad categories:
- Variables can be categorized as continuous or discrete
- Variables van be categorized as quantitative or qualitative

Continuous variable = is measured along a continuum at any place beyond the
decimal point. A continuous variable can thus be measured in fractional units e.g. time for
Olympic sprinters

Discrete variable = is measured in whole units or categories that are not distributed
along a continuum e.g. number of brothers and sisters

Quantitative variable = varies by amount. This variable is measured numerically and is
often collected by measuring or counting

Qualitative variable = varies by class. This variable is often represented as a label and
describes nonnumeric aspects of phenomena (only discrete variables).

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