Question 4 What are data and what do they mean to a scientist?
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Transcript of Question 4 What are data and what do they mean to a scientist?
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Question
What are data and what do they mean to a scientist?
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Dinner at the Urquhart House
Brought to you by the Briggs Multiracial Alliance
Sunday night All food provided (probably Chinese) Contact Mimi Reddy, [email protected]
for details
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Data, Statistics, and Spreadsheets
What are data? What are statistics? What are spreadsheets? How can you analyze data with
spreadsheets?
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Data
Data are pieces of information Data can be numbers, words, descriptions Data have UNITS The word data is PLURAL, datum is singular Data about Willoughby:
• Age: 5 (years)• Height: 47 (inches)• Weight: 66 (pounds)• Eyes: Blue• Favorite word: Wrestle• Favorite letter: W
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Types of Data
Numbers – two types– Real #s – rational numbers – 28.75 lbs– Integers – whole numbers – 18 months
Letters – called characters in programming– W is a character
Words – called strings in programming– “No thanks” is a strings, can be individual
words or phrases
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Statistics and Data
Test Scores: – Jeff: 88
– Mollie: 92
– Marcie: 88
– Dave: 47
– Karim: 99
– Willoughby: 42
– Benjamin: 0
What statistics can you calculate to describe these data?
– Try to think of four things to describe the data
stop
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Statistics
Statistics are derived from the data Statistics are descriptions of data Statistics are meant to simplify the data Statistics can be misleading
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Typical Statistics
Sample Size - number of individuals measured = n
Sum = Average or Mean = /n Median
– Value of 50th percentile, half of values fall above, half below
Maximum, Minimum, Range (Max-Min) Mode - most common value Standard deviation Variance (SD
2)
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Analyze these data...
Mean, max, min, range, median, mode
• 18
• 33
• 4
• 47
• 49
• 38
• 29
• 4
• 55
sample size (n)
Sum
mean=average=/n• denoted x
median = halfway
mode = most common
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Spreadsheets
Spreadsheets are tables
Spreadsheets allow calculations and manipulations of data
• Calculations: mean, standard deviation
• Manipulations: sort,
CostaRica NicaraguaRainforest 625,000 3,712,000Dry Forest 50,000 300,000
Total 675,000 4,012,000
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Make a data table:
Fly 1, length 13.4 mm, velocity 27 Kph, age 21 days Fly 2, length 9.4 mm, velocity 0 Kph, age 220 days Fly 3, length 9.3 mm, velocity 44 Kph, age 1 days Fly 4, length 13.4 mm, velocity 17 Kph, age 32 days Fly 5, length 17.4 mm, velocity 33 Kph, age 11 days
How many columns? How many rows? #s go down or across?
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Data Table
Fly # Length Velocity Age
1
2
3
4
5
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Microsoft Excel
Typical spreadsheet program– Lotus 1-2-3 is original commercial spreadsheet
Has similar controls to MS Word Now allows graphing (charts)
• very restricted formats, hard to get exactly what you want
Excel tables and graphs can be copied into MS Word
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Friday’s Assignment
We will work with Microsoft Excel to analyze some data
Groups of two will submit one finished spreadsheet for the assignment
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Graphs
Many different types of graphs– Points– Lines– Bars– Pies
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Point Graphs
Called X-Y Scatter in MS Excel Plot points based on X and Y value Can fit a “REGRESSION LINE” to the data
– Line that best fits the data
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X-Y Scatter
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Bar Graphs
Categorize data into counts or percents Categories can be descriptive categories
(Windows 98, Windows 2000, …) Can also be numeric categories
– Height: 60-63, 63-66, etc. or just 61, 62, 63…– Count up number of people in each group
Histograms are a particular type of bar graph
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Bar Graph
Starting Salary
$0
$10,000
$20,000
$30,000
$40,000
$50,000
1988 1989 1990 1991 1992 1993 1994
Starting Salary
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Histogram
X axis is categories Y axis is a number or proportion of
observations in that category
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Histogram Bar GraphN
um
ber
of
Cra
shes
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Regular Bar Graph vs. Histogram Bar Graph
Starting Salary
$0
$10,000
$20,000
$30,000
$40,000
$50,000
1988 1989 1990 1991 1992 1993 1994
Starting Salary
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Distributions
Special type of histogram with continuous numeric scale at bottom
Normal distribution is a key concept in statistics
Skewed distribution is one that is unbalanced
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Sample distribution histograms
Danyoungyoo, Katanchalee, and Srichawla, www.s-t.au.ac.th/handout/st2204/week5-Univariate-Des.pptRobert D. Duval, PS 400 Lecture, www.polsci.wvu.edu/duval/ps400/Notes/400Notes.ppt
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The NORMAL Distribution
A NORMAL DISTRIBUTION is the theoretical distribution of values given natural variation around a MEAN
It is balanced, humped distribution
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Distributions
Skew is an imbalance in the distribution
Danyoungyoo, Katanchalee, and Srichawla, www.s-t.au.ac.th/handout/st2204/week5-Univariate-Des.ppt
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Hypothesis Testing
Statistical Tests are how scientists decide if data support their hypothesis
(NOT PROVE their hypothesis) Four major statistical tests: T-test, X2 Test,
Regression, ANOVA
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Hypothesis
Processor speed has an effect on the performance of the computer.
Null Hypothesis– H0: Processor speed has NO EFFECT on the
performance of a computer.
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Statistical Tests and Probability
Statistical tests give a value That value can be related to a probability Probability is likelihood that NULL
hypothesis is correct given the data you have
If P < 0.05 (1/20), then you conclude NULL hypothesis is FALSE
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T-Test
Compares differences between two means
Formula: T = (x1-x2)/SEM
– SEM is Standard Error of Mean [SD/(N-1)]
T Values: Difference between mean in comparison to the amount of spread in your data
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T-Values
If T > 2.5 or 3.0, difference is usually significant (this depends on your sample sizes)