Transcript ppt - Perimeter College Sites

The Power of Technology:
Using the TI-83/84 and Excel in Statistics
Keisha Brown
Perimeter College at Georgia State University
[email protected]
www.sites.pc.gsu.edu/klanier
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
1
Why the TI-84 AND Excel? – AP Statistics
College Board
• “A graphing calculator is a useful computational aid, particularly in analyzing
small data sets, but should not be considered equivalent to a computer in the
teaching of statistics.”
• “Because the computer is central to what statisticians do, it is considered
essential for teaching the AP Statistics course. However, it is not yet possible
for students to have access to a computer during the AP Statistics Exam.”
• “The computer does more than eliminate the drudgery of hand computation
and graphing — it is an essential tool for structured inquiry.”
2
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Why the TI-84 AND Excel? – American
Statistical Association’s GAISE
• “We think technology should be used to analyze data, allowing students to focus on
interpretation of results and testing of conditions, rather than on computational
mechanics. Technology tools should also be used to help students visualize concepts
and develop an understanding of abstract ideas by simulations.”
• “Regardless of the tools used, it is important to view the use of technology not just
as a way to compute numbers but as a way to explore conceptual ideas and enhance
student learning as well. We caution against using technology merely for the sake of
using technology (e.g., entering 100 numbers in a graphing calculator and calculating
statistical summaries) or for pseudo-accuracy (carrying out results to multiple
decimal places).”
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Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Indeed.com
Search for Graphing Calculator
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Search for Excel
8,379
4
What Other Tools Are Out There?
Infographic source: http://www.predictiveanalyticstoday.com/top-statistical-software/
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Statcrunch
Tinkerplots
Tableau
Excel Add-Ins
Tablet Apps
Fathom
Codap
TuvoLabs
NZGrapher
Plotly
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Before you begin, you need to check:
Graphing Calculator
•
•
•
•
What operating system do they have?
2nd, plus (MEM), 1:About
TI-84 Plus CE – 5.1.5
TI-84 Plus, TI-84 Plus Silver Edition
2.55MP is the newest operating system
• Is their StatWizard off or on?
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Excel
• Do they have a PC or a Mac?
• Which version of Excel do they
have?
• Do they have the Data Analysis
Tool Pak installed?
• File, Options, Add-Ins, Go
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How to import/enter/share your data
Graphing Calculator
Excel
Video
Or manually type it in
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
7
Random Sampling
TI-83/84
Excel 2013
• Randomly select and set a seed.
• (I chose 34.)
• =rand()
• =randbetween(min, max)
• Data Tab, Data Analysis, Random
Number Generation
• Select your sample.
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
8
Descriptive Statistics
Mean, Sample Standard Deviation, Population standard deviation, 5 Number Summary (min, Q1, Q2, Q3, max)
TI-84
Stat, CALC, 1:1-Var Stats, (Select List - OPTIONAL)
Excel
Type individual function names
Mean = average(data)
Or
Data, Data Analysis, Descriptive Statistics
*Make sure to select Summary Statistics*
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
9
Graphs for One Variable
Histogram, Box Plot with Outliers, Box Plot Without Outliers, Dot Plot, Stem and Leaf Plot
TI-84
Excel
*Data, Data Analysis, Histogram*
Right click on a bar for format data series
N/A
N/A
N/A
N/A
N/A
Insert, Column Chart
Insert, Pie Chart
N/A
Data, Data Analysis, Regression
Select Normal Probability Plot at the bottom
Histogram
Box Plot with Outliers
Box Plot without Outliers
Bar Chart
Pie Chart
Dot Plot, Stem and Leaf Plot,
Normal Probability Plots
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
10
Bivariate Data
TI-84
Excel
Turn on Diagnostic, so students will see the
additional menus. 2nd, 0 (Catalog), DiagnosticOn
ScatterPlot
r, r2, least squares
regression line
Keisha Brown
Stat, Calc, 4:LinReg(ax+b)
[email protected]
http://sites.pc.gsu.edu/klanier
Highlight your columns first.
Insert, Scatterplot.
=correl(x, y)
=rsq(y, x)
=slope(y, x)
=intercept(y,x)
OR
DATA, Data Analysis, Regression
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Probability Distributions –Discrete
Excel
TI-83/84
• For the new operating system, make sure
the STATWIZARDS are off
• Link
• Stat, 1:1-Var Stats L1, L2
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
12
Probability Distributions –Binomial
TI-83/84
Excel
Binompdf(n, p, x) – What is the
probability of getting x successes
from n trials with a probability of
success p?
1.) What is the probability of getting a 100 on a 10
question multiple choice (A – D) quiz that you did not
study for?
Binomcdf(n, p, x) – What is the
probability of getting x or less
successes from n trials with a
probability of success p?
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
2.) What is the probability of failing this quiz?
3.) What is the probability of scoring between a 70 and
90, inclusive?
13
Probability Distributions –Normal
Excel
TI-83/84
Normalcdf(lowerlimit, upper limit, mean, std. dev.)
invNorm(area to the left, mean, std. dev.)
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
14
Probability Distributions –Student’s t Distribution
TI-83/84
Excel
To find the probability
Tcdf(lower limit, upper limit, df)
To find the probability
=t.dist(test statistic, df, true)
To find the critical values
invT(α , df)
To find the critical values
t.inv(α, df)
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
15
Confidence Intervals (Means)
TI-84
Excel
Confidence Interval for a Population Mean
(σ is known)
Confidence Interval for a Population Mean
(σ is NOT known and normal population)
Confidence Interval for a Difference between means
(unpaired)(𝝈𝟏 𝒂𝒏𝒅 𝝈𝟐 are known)
Stat, TESTS, Z-interval
*Gives the margin of error*
=confidence.norm(α, σ, n)
*Gives the margin of error*
=confidence.t(alpha, s, n)
Confidence Interval for a Difference between means
(unpaired) (𝝈𝟏 = 𝝈𝟐 and are unknown)
Stat, TESTS, 2-SampTInt (pool the
variance)
Confidence Interval for a Difference between means
(unpaired) (𝝈𝟏 ≠ 𝝈𝟐 and are unknown)
Stat, TESTS, 2-SampTInt (do not pool
the variances)
Confidence Interval for a Difference between means
(paired)
Put data in L1 and L2.
In L3, calculate the difference.
Stat, TESTS, T-interval(L3)
Keisha Brown
[email protected]
Stat, TESTS, T-interval
Stat, TESTS, 2-SampZInt
http://sites.pc.gsu.edu/klanier
Manual
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Confidence Intervals (Proportions and Slope)
TI-84
Excel
Confidence Interval for a Population Proportion (p)
Stat, TESTS, 1-PropZInt
Manual
Confidence interval of the difference of two
independent proportions
Stat, TESTS, 2-PropZInt
Confidence Interval for the slope of a least-squares
regression line
LinRegTInt
Keisha Brown
[email protected]
http://sites.pc.gsu.edu/klanier
Data, Data Analysis, Regression
*Make sure to select the Confidence
Level
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Hypothesis Testing (Means and Proportions)
Hypothesis Testing For a Population Mean
(σ is known) n ≥ 30
Hypothesis Testing For a Population Mean
(σ is unknown) n ≤ 30
Hypothesis Testing For a 2 Independent Means
(σ1 and σ2 is known) n1 and n2 ≥ 30
Hypothesis Testing with 2 Independent Means
(σ1 and σ2 are unknown)
TI-84
Stat, TESTS, Z-test
Stat, TESTS, T-test
Stat, TESTS, 2-SampZTest
DATA, Data Analysis, z-Test: Two-Sample Means
Stat, TESTS, 2-SampTTest
=t.test(array1, array2, tails, type)
If σ1 = σ2 , pooled variances = “yes”
If σ1 ≠ σ2 , pooled variances = “no”
Hypothesis Testing with 2 Dependent Means
Excel
Put data in L1 and L2.
Calculate the difference in
L3. Stat, TESTS, TTest(L3)
Tails = 1 if a one-sided test, 2 if two-sided test
Type = 2 if two-sample equal variance(homoscedastic), 3
if two-sample unequal variance (heteroscedastic)
OR
DATA, Data Analysis, t-Test: Two-Sample Assuming Unequal
Variances
OR
DATA, Data Analysis, t-Test: Two-Sample Assuming Equal
Variances
=t.test(array1, array2, tails, type)
Tails = 1 if a one-sided test, 2 if two-sided test
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Type = 1
OR
DATA, Data Analysis, t-Test: Paired Two-Sample for Means
Hypothesis Testing (Proportions)
TI-84
Hypothesis Testing For a Population Proportion Stat, TESTS, 1-PropZTest
Hypothesis Testing with 2 Population
Proportions
Keisha Brown
[email protected]
Excel
Manual
Stat, TESTS, 2-PropZTest
http://sites.pc.gsu.edu/klanier
19
Hypothesis Testing (Others)
TI-84
Excel
Chi-Square Test of Independence
Stat, TESTS, 𝜒 2 − 𝑇𝑒𝑠𝑡
=chisq.test(observed, expected)
Chi-Square Goodness of Fit Test ***
Stat, TESTS, 𝜒 2 𝐺𝑂𝐹 − 𝑇𝑒𝑠𝑡
=chisq.test(observed, expected)
L1: Observed Counts
L2: Expected Counts
Stat, TESTS, 2-SampFTest
Data, Data Analysis, F-Test Two-Sample for Variance
Hypothesis Tests for Variance
*Data with the largest variance goes in list
1.
ANOVA (3 or more µs)
Test for the slope of a least-squares
regression line
Keisha Brown
[email protected]
Stat, TESTS, Anova(
Stat, TESTS, LinRegTTest
http://sites.pc.gsu.edu/klanier
*Data, Data Analysis, ANOVA: Single Factor
*Data, Data Analysis, ANOVA: Two-Factor with
Replication
*Data, Data Analysis, ANOVA: Two-Factor without
Replication
Data, Data Analysis, Regression
Make sure to select the Confidence Level
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