Intro to Statistics! - WordPress.com · Intro to Statistics! Mythvestigations. What is Statistics?...
Transcript of Intro to Statistics! - WordPress.com · Intro to Statistics! Mythvestigations. What is Statistics?...
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Intro to Statistics!Mythvestigations
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What is Statistics?
And why do we need it?
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Types of Data● Quantitative
○ A numerical description
■ Temperature, height, etc.
● Qualitative○ Describes a quality:
■ Color, type of product, etc.
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vs Observational
● Does not assign treatment
groups
● Cannot keep factors constant
● Good for when assigning
treatments is implausible or
unethical/illegal
Experimental
● Applies treatments to a group
and measures the effects
● Has a control and treatment
● Strongly preferred over
observational studies,
especially for science fairs
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For example...
An OBSERVATIONAL STUDY would be taking a group of people currently taking vitamins and a group of people not taking vitamins and comparing their health status. (these people were taking vitamins beforehand)
An EXPERIMENTAL STUDY would be randomly selecting a group of, say, 60 people, splitting them up randomly into two 30-person groups, and assigning one group to take vitamins and the other group to not.
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VariablesCategorical
● Binary● Nominal● Ordinal
Quantitative
● Continuous● Ratio
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Limitations of Data Collection
Quantitative
● Clear, specific, and can easily be shown graphically
● Complex statistical analysis
● Limited response options
Qualitative
● Patterns of behavior and further explanation
● May not represent population
● Time consuming and evaluator bias
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General Tips for Data Collection
● The more data, the better!● Randomize
○ Random samples give accurate results○ If you’re experimenting on people, random selection is
almost impossible, but try to get a varied sample - not just friends and family
● Add dates/times to all your data recordings● Stratification/blocking depending on your data
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Qualitative Graphs● Bar Graph
○ Shows number of data in
each category
● Pie Chart/Circle Graph
○ Shows data as
percentages/proportions/
parts of a whole
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Quantitative Graphs● Scatter Plots
○ Show correlation
● Histogram
○ Interval for each bar
● Line Graph
○ Change over time
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Descriptive Statistics
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Measures of Central Tendency
● Mean○ Average value
● Median○ “Middle” value
● Mode○ Most frequently occurring value
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Mean
● The “average”● Can easily be affected by outliers● Found by adding all values and dividing by the
number of data points
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What are outliers?● Data points that are far beyond the spread of the rest of
the data
○ Be careful when using mean
● Can be excluded in analysis
○ You must EXPLICITLY state that you are excluding
data when drawing conclusions
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Standard Deviation
● The average distance that a data point is from the mean
● Square root of another value called the variance
● Represented by σ (sigma)● You can use a TI-83/84, Excel, or
an online calculator to find this
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Sample Standard Deviation
● When doing statistical testing, you may need to know the standard deviation
● Usually only a SAMPLE of data is taken from a group, which means you have to use the sample standard deviation, s
● Represents a generalized result to the ENTIRE POPULATION
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Standard Error
● Measure of the statistical accuracy
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Statistical Tests
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Confidence Intervals
● 95% confidence intervals● Chance that results and correlations aren’t a coincidence● Mean ± 2 standard error
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ANOVA
● Three or more independent groups● Null + Alternative hypothesis
Example of format
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T-Test
● One sample vs Two sample● One-tailed vs two-tailed
○ One tailed for when you want to see if there is a difference in one direction (< or >)
○ Two tailed for when you want to see if there is a difference in either direction (≠)
● Paired T-Test○ Whether there is a difference between means where you
have two samples that are related/paired○ For example, before and after experiments have paired
values
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Chi-Squared
● Used for the comparison of two categorical variables to see if there is significant association.
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Chi-Squared Cont.
1. Chi-squared test statistic2. Degrees of freedom
a. Number of categories-1
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Now, let’s see how much you know!