# Statistics by gjjur4356

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```									                 Statistics
Variable
Anything that can have more than one
value
ie. Height, weight, sex, IQ, video games

Constant
Anything that remains the same
ie. Study on females (females remains
constant)
Statistics cont.
Utilizes the organization of raw data that has
already been collected
Expressed in different ways:
1. Histogram (Bar graph)
x axis (abscissa) - horizontal
y axis (ordinate) - vertical
2. Pie Chart
3. Polygon (Line graph)
Which class performed better?

Class A                                  Class B

90                                        90

75

85                                        60

45
% on test                                % on test
80                                        30

15

75                                        0
Ss 1   Ss2   Ss3   Ss4                    Ss1   Ss2   Ss3   Ss4
Measurement Scales
Nominal Scale:
numbers are used to name or categorize
(ie. Sports uniforms, gender,driver’s licence)

Ordinal Scale:
numbers represent serial position
(ie. Finish in a race, rankings, level of
aggression)
Measurement Scales cont.
Interval Scale:
consistent units if measurement and equal
spacing between units (no true zero point)
ie. Celcius

Ratio Scale:
Same as interval, but has absolute zero point
ie. Weight, height, time, distance
Types of Statistics
Descriptive Statistics
- A statistic to describe behaviour
- ie. SAT scores

Inferential Statistics
- A statistic that explains behaviour
- Bandura’s Bobo doll experiment on aggression
- example: t-test or ANOVA (analysis of variance)
Measures of Central Tendencies
A single score that represents a whole
set of scores

Mode: Most frequently occurring score

Median: Middle score (half above and below)

Mean: Arithmetic average (most widely used)
Skewed statistics
When the data is not distributed evenly,
atypical scores can mislead the data

Always be aware of the measure of central
tendency that people are reporting
Income data
\$20,000
\$22,000
\$23,000
\$28,000
What is the Mode?
\$34,000
\$38,000
\$41,000       What is the Median?
\$42,000
\$44,000
\$85,000
\$90,000
What is the Mean?
\$210,000
\$210,000
Normal Curve (Bell Curve)
Theoretical or hypothetical frequency of
scores

68% between 1 and -1 SD
95% between 2 and -2 SD
99% between 3 and -3 SD

Examples: height, weight, IQ
Variability
The amount of variability between scores tells us the reliability
of the data
The lower the variability the more reliable the results

Basketball player example

Range: The gap between the lowest and the highest score

Crude estimate of variability based on extreme scores
Standard Deviation
- Standard measurement of how the scores in a
distribution deviate from the mean

- Better way to assess level of variability between
scores

- Represented by lower case s
- ie. UBC vs. Kwantlen entrance marks
who has the smaller SD?
When is an observed difference
reliable?
1. Representative vs. Biased Sample
Is it random and large enough?

2. Less variable observations are more
reliable

3. More cases are better
ie. Assessing which school is better?
Statistical Significance
- Statistical statement of how likely it is that an
obtained result occurred by chance

- p<.05
- “beyond a reasonable doubt”

- indicates the likelihood the result will happen by
chance
- Does not indicate IMPORTANCE of result
- ie. IQ between first born and second born
Reliability & Validitiy
 Reliability is the extent to which an
experiment, test, or any measuring
procedure yields the same result on
repeated trials.
 Validity refers to the degree to which a
study accurately reflects or assesses the
specific concept that the researcher is
attempting to measure.
Reliability & Validity
 While reliability is concerned with the
accuracy of the actual measuring
instrument or procedure, validity is
concerned with the study's success at
measuring what the researchers set out to
measure.
Reliability & Validity
Correlation Coeffiecient
Measures relationship between two
variables
- data must be interval or ratio

Pearson Product-Moment Correlation is
represented by small case r
remember…
If anything is paid attention to in our schools,
colleges, and universities, thinking must be it.
Unfortunately, thinking can be lazy. It can be
sloppy….It can be fooled, misled, bullied...
Students possess great untrained and untapped
capacities for logical thinking, critical analysis,
and inquiry, but these are capacities that are not
spontaneous: They grow of wide instruction,
experience, encouragement, correction, and
constant use.
Experiment
Information:
The Nestle Inc. authoritatively states that
Smarties are 25% pink, 20% green, 15%
brown,15% yellow, 15% orange, and 10%
purple. This distribution is important for
“quality control”.

Is this true? Are they that accurate?
Sample
Three random boxes of mini Smarties. All boxes
are still originally sealed and have not been
tampered with.

Design a data sheet and complete your data
collection. (Ensure that you complete your data
before premature subject mortality occurs!)

Convert raw data into percentages
Hypothesis

Develop a hypothesis based on the
distribution of the data you collected
Proving your hypothesis
Join up with two other classmates and
integrate your data.

Is your hypothesis still right?

Do you have a new hypothesis?

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