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?
Question
What are data and what do they mean to a scientist?
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
Data, Statistics, and Spreadsheets
What are data? What are statistics? What are spreadsheets? How can you analyze data with
spreadsheets?
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
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
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
Statistics
Statistics are derived from the data Statistics are descriptions of data Statistics are meant to simplify the data Statistics can be misleading
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)
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
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
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?
Data Table
Fly # Length Velocity Age
1
2
3
4
5
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
Friday’s Assignment
We will work with Microsoft Excel to analyze some data
Groups of two will submit one finished spreadsheet for the assignment
Graphs
Many different types of graphs– Points– Lines– Bars– Pies
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
X-Y Scatter
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
Bar Graph
Starting Salary
$0
$10,000
$20,000
$30,000
$40,000
$50,000
1988 1989 1990 1991 1992 1993 1994
Starting Salary
Histogram
X axis is categories Y axis is a number or proportion of
observations in that category
Histogram Bar GraphN
um
ber
of
Cra
shes
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
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
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
The NORMAL Distribution
A NORMAL DISTRIBUTION is the theoretical distribution of values given natural variation around a MEAN
It is balanced, humped distribution
Distributions
Skew is an imbalance in the distribution
Danyoungyoo, Katanchalee, and Srichawla, www.s-t.au.ac.th/handout/st2204/week5-Univariate-Des.ppt
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
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.
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
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
T-Values
If T > 2.5 or 3.0, difference is usually significant (this depends on your sample sizes)