Introduction to Statistical Analysis Using Graphpad Prism 6

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Page 1: Introduction to Statistical Analysis Using Graphpad Prism 6

Graphpad Prism 6

Introduction

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Page 2: Introduction to Statistical Analysis Using Graphpad Prism 6

Download & Install

• You can download and install 30 days

evaluation version from

http://www.graphpad.com/demos/

• Upon installation, do not start the evaluation • Upon installation, do not start the evaluation

period unless you are ready to start using it

immediately.

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Page 3: Introduction to Statistical Analysis Using Graphpad Prism 6

Uniqueness of Prism

• Prism caters for analysis and graphs for scientific

publication, especially for laboratory and

biomedical research.

• Data are usually entered and manipulated using • Data are usually entered and manipulated using

spreadsheet such as Microsoft Excel. Data

needed for analysis are copied into specific tables

within Prism.

• Specific analysis requires specific tables. So you

must know exactly what analysis is required.

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Page 4: Introduction to Statistical Analysis Using Graphpad Prism 6

The 6 tables within Prism.

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Page 5: Introduction to Statistical Analysis Using Graphpad Prism 6

XY Data Tables

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Column tables

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Grouped tables

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Contingency tables

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Survival tables

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Parts of whole tables

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Page 11: Introduction to Statistical Analysis Using Graphpad Prism 6

Choosing the appropriate

statistical testsstatistical tests

Use these tables to choose the

appropriate statistical tests.

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Page 12: Introduction to Statistical Analysis Using Graphpad Prism 6

Parametric Statistical Tests

Qualitative

Dichotomus

Quantitative Normally distributed data Student's t Test

Qualitative

Polinomial

Quantitative Normally distributed data ANOVA

Quantitative Quantitative Repeated measurement of the Paired t TestQuantitative Quantitative Repeated measurement of the

same individual & item (e.g.

Hb level before & after

treatment). Normally

distributed data

Paired t Test

Quantitative -

continous

Quantitative -

continous

Normally distributed data Pearson Correlation

& Linear

Regresssion

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Page 13: Introduction to Statistical Analysis Using Graphpad Prism 6

Non-parametric Statistical Tests

Qualitative

Dichotomus

Quantitative Data not normally distributed Wilcoxon Rank Sum

Test or U Mann-

Whitney Test

Qualitative Quantitative Data not normally distributed Kruskal-Wallis One Qualitative

Polinomial

Quantitative Data not normally distributed Kruskal-Wallis One

Way ANOVA Test

Quantitative Quantitative Repeated measurement of the

same individual & item

Wilcoxon Rank Sign

Test

Quantitative -

continous/ordina

l

Quantitative -

continous

Data not normally distributed Spearman/Kendall

Rank Correlation

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Page 14: Introduction to Statistical Analysis Using Graphpad Prism 6

Statistical Tests for Qualitative Data

Variable 1 Variable 2 Criteria Type of Test

Qualitative Qualitative Sample size > 20 dan no

expected value < 5Chi Square Test (X

2)

Qualitative Qualitative Sample size > 30 Proportionate TestQualitative

Dichotomus

Qualitative

Dichotomus

Sample size > 30 Proportionate Test

Qualitative

Dichotomus

Qualitative

Dichotomus

Sample size > 40 but with at

least one expected value < 5X

2 Test with Yates

Correction

Qualitative Quantitative Normally distributed data Student's t TestQualitative

Dichotomus

Qualitative

Dichotomus

Sample size < 20 or (< 40 but

with at least one expected

value < 5)

Fisher Test

Qualitative Quantitative Data not normally distributed Wilcoxon Rank Sum

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Page 15: Introduction to Statistical Analysis Using Graphpad Prism 6

Prism Hands-on Exercise

http://drtamil.me

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Page 16: Introduction to Statistical Analysis Using Graphpad Prism 6

URL for data & submit answers

• Data -https://drive.google.com/file/d/0B_0qI7iLxVpmVWNXMnV3WWZMSWM/view?usp=sharing

• The analysis required http://drtamil.me/2015/02/04/uninottichallengehttp://drtamil.me/2015/02/04/uninottichallenge/ password tcr1 (exercise done at teaching computer room 1 – tcr1)

• Submit answers at this link https://docs.google.com/forms/d/1o_L7ZjXF9Q1PON2zDs_VwkKsLCHT4v-8WruXhCiVq2Q/viewform

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Page 17: Introduction to Statistical Analysis Using Graphpad Prism 6

Data – Factors Related to SGA

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Page 18: Introduction to Statistical Analysis Using Graphpad Prism 6

A study to identify factors that can cause small for gestational

age (SGA) was conducted. Among the factors studied were the

mothers’ body mass index (BMI). It is believed that mothers with

lower BMI were of higher risk to get SGA babies.

• 1. Create a new variable mBMI (Mothers’ Body Mass Index) from the mothers’ HEIGHT (in metre) & WEIGHT (first trimester weight in kg). mBMI = weight in kg/(height in metre)2. Calculate the following for mBMI;

– Mean

– Standard deviation

• 4. Conduct the appropriate statistical test to test whether there is any association between BMI and OUTCOME.

• 5. Conduct the appropriate statistical test to find any association between OBESCLAS (Underweight/Normal/Overweight) and BIRTHWGT.

• 6. Assuming that both variables mBMI & – Standard deviation

• 2. Create a new variable OBESCLAS (Classification of Obesity) from mBMI. Use the following cutoff point;

– <20 = Underweight

– 20 – 24.99 = Normal

– 25 or larger = Overweight

– Create a frequency table for OBESCLAS.

• 3. Conduct the appropriate statistical test to test whether there is any association between OBESCLAS (Underweight/ Normal/Overweight) and OUTCOME.

• 6. Assuming that both variables mBMI & BIRTHWGT are normally distributed, conduct an appropriate statistical test to prove the association between the two variables.

– Demonstrate the association using the appropriate chart. Determine the coefficient of determination.

• 7. Conduct Simple Linear Regression using BIRTHWGT as the dependent variable. Try to come out with a formula that will predict the baby’s birthweight based on the mother’s BMI.

– y = a + bx

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Online form for answers

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Page 20: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 1 & 2

• 1. Create a new variable mBMI (Mothers’ Body Mass Index) from the mothers’ HEIGHT (in metre) & WEIGHT (first trimester weight in kg). mBMI = weight in kg/(height in metre)2. Calculate the following for mBMI;– Mean

– Standard deviation– Standard deviation

• 2. Create a new variable OBESCLAS (Classification of Obesity) from mBMI. Use the following cutoff point;– <20 = Underweight

– 20 – 24.99 = Normal

– 25 or larger = Overweight

– Create a frequency table for OBESCLAS.

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Page 21: Introduction to Statistical Analysis Using Graphpad Prism 6

Compute BMIDrag down to

fill up the cells

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Page 22: Introduction to Statistical Analysis Using Graphpad Prism 6

Recode BMI into OBESCLAS

• Type

=IF(F2<20,"Underweigh

t",IF(F2>25,"Overweight

","Normal")) in cell G2

and press Enter.and press Enter.

• Then drag down cell G2

until G101 to fill up the

rest of the cells.

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Page 23: Introduction to Statistical Analysis Using Graphpad Prism 6

Recode BMI into OBESCLAS

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Recode BMI into 1,2 or 3

• We should also recode BMI into numeric OBESCLAS2 for import into Prism. Prism doesn’t accept string data.accept string data.

• =IF(F2<20,“1",IF(F2>25,“3",“2")) in cell H2 and press Enter.

• Then drag down cell H2 until H101 to fill up the rest of the cells.

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Page 25: Introduction to Statistical Analysis Using Graphpad Prism 6

Recode BMI into 1,2 or 3

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Page 26: Introduction to Statistical Analysis Using Graphpad Prism 6

Recode BMI into OBESCLAS

• If typing logical command is not your forte, you can

just select all data, then sort the data according to

the BMI. Then drag and fill values 1, 2 or 3 beside it.

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Page 27: Introduction to Statistical Analysis Using Graphpad Prism 6

Add Column Freq with Value of 1

• Just add another

column with the

variable name “FREQ”

and fill it with value of 1

from I2 to I100.from I2 to I100.

• This will help with the

pivot table exercise

later.

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Page 28: Introduction to Statistical Analysis Using Graphpad Prism 6

Import Excel Data Into Prism

• Select all the data from

Excel. Copy.

• Open Prism, select

“Columns”, “Enter

replicate values..” &

click “Create”

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Page 29: Introduction to Statistical Analysis Using Graphpad Prism 6

Paste Into Prism

• Click the cell between

“Group A” and row Y

and paste.

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Page 30: Introduction to Statistical Analysis Using Graphpad Prism 6

Checking Normality

• Click on the “Analyze”

button.

• Select “Column

Statistics”.Statistics”.

• Select the variables

with continuous data.

• Then click “OK”.

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Page 31: Introduction to Statistical Analysis Using Graphpad Prism 6

Click on the following;

• Test if the

values from

a Gaussian

distribution.

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Page 32: Introduction to Statistical Analysis Using Graphpad Prism 6

Only Height is normally distributed

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But for the purpose of today’s exercise, we are going to ASS-U-ME that all

these continuous variables are normally distributed.

Page 33: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 1 – BMI

• Column Statistics also

generates the Mean &

S.D.;

– Mean 24.49

– S.D. 4.769

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Page 34: Introduction to Statistical Analysis Using Graphpad Prism 6

Frequency Distribution

• Go back to the data by clicking on the data table on left side of screen. Then click on the “Analyze” button the “Analyze” button again.

• Select “Frequency Distribution”

• Tick on OBESCLAS2. Then click on “OK”.

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Page 35: Introduction to Statistical Analysis Using Graphpad Prism 6

Frequency Distribution

• Then click on OK again.

You will get the

following frequency

distribution table.

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Page 36: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 2 – Obese Classification

• UW – 17%

• N – 40%

• OW – 43%

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Page 37: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 3

• 3. Conduct the appropriate statistical test to test whether there is any association between OBESCLAS

SGA Normal TOTAL

UnderW

Normal

OverW

TOTAL 50 50 100between OBESCLAS (Underweight/Normal/Overweight) and OUTCOME.

• Therefore most suitable analysis is Pearson Chi-square.

TOTAL 50 50 100

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Variable 1 Variable 2 Criteria Type of Test

Qualitative Qualitative Sample size > 20 dan no

expected value < 5Chi Square Test (X2)

Qualitative

Dichotomus

Qualitative

Dichotomus

Sample size > 30 Proportionate Test

Qualitative

Dichotomus

Qualitative

Dichotomus

Sample size > 40 but with at

least one expected value < 5X

2 Test with Yates

Correction

Qualitative Quantitative Normally distributed data Student's t TestQualitative

Dichotomus

Qualitative

Dichotomus

Sample size < 20 or (< 40 but

with at least one expected

value < 5)

Fisher Test

Qualitative Quantitative Data not normally distributed Wilcoxon Rank Sum

Page 38: Introduction to Statistical Analysis Using Graphpad Prism 6

Pivot Table in Excel

• Click on “Insert”, “Pivot

Table” in Excel.

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• Select all your earlier

Excel data.

Page 39: Introduction to Statistical Analysis Using Graphpad Prism 6

Pivot Table

• On the right side of the screen, pull FREQ into values, OBESCLAS into row labels and OUTCOME into column labels.

• Now select the created contingency table (excluding the “Grand Total”), and copy it using Ctrl-C.

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Page 40: Introduction to Statistical Analysis Using Graphpad Prism 6

Paste Pivot Table Into Prism

• Click “New”, “New Data Table”.

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Table”.

• Select “Contingency”, “Start with an empty table”.

• Then paste the pivot table into Prism.

Page 41: Introduction to Statistical Analysis Using Graphpad Prism 6

The Pasted Pivot Table

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Page 42: Introduction to Statistical Analysis Using Graphpad Prism 6

Chi-Square Analysis

• Click on “Analyze”, “Contingency

table analysis”, then “Chi-

square”, then OK again twice.

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Page 43: Introduction to Statistical Analysis Using Graphpad Prism 6

Chi-Square Results from Prism

Normal Overweight Underweight0

20

40

60

Contingency

Fre

qu

en

cy

Normal

SGA

• Prism only states that there is a significant association (p < 0.0001) between mother’s weight classification and small for gestational age.

• But it doesn’t show which group has the higher rate of SGA.

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Normal Overweight Underweight

Mothers' Weight Classification

Page 44: Introduction to Statistical Analysis Using Graphpad Prism 6

Combine Results From Excel & Prism

• There is a significant difference (p<0.0001) of SGA rates

between underweight, normal and overweight mothers.

• Underweight mothers has a higher rate (94%) of SGA,

compared to normal mothers (58%) and overweight

mothers (26%).

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Page 45: Introduction to Statistical Analysis Using Graphpad Prism 6

Underweight vs Normal?

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• There is a significant difference (p<0.01) of SGA rates between underweight and normal mothers.

• Underweight mothers has a significantly higher rate (94%) of SGA, compared to normal mothers (58%).

Page 46: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 3

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Page 47: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 3

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Page 48: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 4

• 4. Conduct the appropriate statistical test to test whether there is any association between BMI and OUTCOME.

Qualitative

Dichotomus

Quantitative Normally distributed data Student's t Test

Qualitative

Polinomial

Quantitative Normally distributed data ANOVA

Quantitative Quantitative Repeated measurement of the Paired t TestBMI and OUTCOME.

• Basically we are comparing the mean BMI of SGA mothers against BMI of Normal mothers.

• Therefore the appropriate test is Student’s t-test.

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Quantitative Quantitative Repeated measurement of the

same individual & item (e.g.

Hb level before & after

treatment). Normally

distributed data

Paired t Test

Quantitative -

continous

Quantitative -

continous

Normally distributed data Pearson Correlation

& Linear

Regresssion

Page 49: Introduction to Statistical Analysis Using Graphpad Prism 6

Copy BMI Column Into Prism

• Click “New”, “New Data Table”.

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Table”.

• Select “Column”, “Enter replicate values into stacked columns”.

• Then paste the BMI of SGA mothers into column A & BMI of Normal mothers into column B.

Page 50: Introduction to Statistical Analysis Using Graphpad Prism 6

The Pasted BMI Data

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Page 51: Introduction to Statistical Analysis Using Graphpad Prism 6

Student’s T-Test

• Click on “Analyze”, “Column

analysis”, then “t-tests”, then

OK again.

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• Tick “Unpaired”, “Yes, parametric”, then “equal SDs”, then OK again.

Page 52: Introduction to Statistical Analysis Using Graphpad Prism 6

T-Test Results from Prism

• Prism states that there is a significant mean difference of BMI (p < 0.0001) between SGA mother’s (22.52) and normal mothers (26.46). normal mothers (26.46). Therefore mean BMI of SGA mothers is significantly lower than the normal mothers.

• And it also proves that there is equal variances of the two means.

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Page 53: Introduction to Statistical Analysis Using Graphpad Prism 6

BM

I

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Page 54: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 4

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Question 4

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Page 56: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 5

• 5. Conduct the appropriate statistical test to find

any association between OBESCLAS

(Underweight/Normal/Overweight) and

BIRTHWGT.BIRTHWGT.

• Basically we are comparing the mean

BIRTHWEIGHT of underweight mothers, normal

weight mothers and overweight mothers.

• Therefore the appropriate test is Analysis of

Variance (ANOVA).

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Page 57: Introduction to Statistical Analysis Using Graphpad Prism 6

Sort Excel Data By

BMI To Facilitate

Copy & Paste

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Page 58: Introduction to Statistical Analysis Using Graphpad Prism 6

Copy Birth Weight Column Into Prism

• Click “New”, “New Data Table”.

• Select “Column”, “Enter replicate

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• Select “Column”, “Enter replicate values into stacked columns”.

• Then paste the babies’ birth weight of underweight mothers into column A, babies’ birth weight of normal weight mothers into column B & babies birth weight of overweight mothers in column C.

Page 59: Introduction to Statistical Analysis Using Graphpad Prism 6

The Pasted Birth Weight Data

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Page 60: Introduction to Statistical Analysis Using Graphpad Prism 6

ANOVA

• Click on “Analyze”, “Column

analysis”, then “One-way

ANOVA”, then OK again.

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• Tick “No matching”, “Yes, ANOVA”, then click “MultipleComparison” tab. Click OK

Page 61: Introduction to Statistical Analysis Using Graphpad Prism 6

ANOVA – post hoc

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Click OK

Page 62: Introduction to Statistical Analysis Using Graphpad Prism 6

ANOVA Results from Prism

• Prism states that there is a significant mean difference of mean birth weight (p < 0.0001) between underweight mothers’ (2.187), normal mothers ‘(2.768) & overweight mothers’(3.245).

• Unfortunately it also proves that there is unequal variances of the three means. So it fails the homogeneity of variances assumption.

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Page 63: Introduction to Statistical Analysis Using Graphpad Prism 6

ANOVA Results – post hoc

• Post-hoc tests indicate there is significant difference of birth weight between ALL the three groups. Underweight mothers’ have the lowest mean birth weight of 2.187kg.

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Page 64: Introduction to Statistical Analysis Using Graphpad Prism 6

3

4

5

ANOVA

h w

eig

ht

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Underweight Normal Overweight0

1

2

Compare Babies Birth Weight byMother's Weight

Bir

th

Page 65: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 5

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Page 66: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 5

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Page 67: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 6

• 6. Assuming that both variables mBMI & BIRTHWGT are normally distributed, conduct an appropriate statistical test to prove the statistical test to prove the association between the two variables.–Demonstrate the association using the

appropriate chart. Determine the coefficient of determination.

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Page 68: Introduction to Statistical Analysis Using Graphpad Prism 6

Pearson Correlation

Qualitative

Dichotomus

Quantitative Normally distributed data Student's t Test

Qualitative

Polinomial

Quantitative Normally distributed data ANOVA

Quantitative Quantitative Repeated measurement of the

same individual & item (e.g.

Hb level before & after

treatment). Normally

distributed data

Paired t Test

Quantitative -

continous

Quantitative -

continous

Normally distributed data Pearson Correlation

& Linear

• mBMI and birth weight are both normally distributed

continuous data. Since the aim is to measure the

strength and direction of the association between

these two continuous variable, therefore Pearson

Correlation is the most appropriate test.

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continous continous & Linear

Regresssion

Page 69: Introduction to Statistical Analysis Using Graphpad Prism 6

Copy BMI & Birth Weight Into Prism

• Click “New”, “New Data

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• Click “New”, “New Data Table”.

• Select “XY”, “Enter and plot a single Y value for each point”.

• Then paste the BMI into column X & BIRTHWGT into column A.

Page 70: Introduction to Statistical Analysis Using Graphpad Prism 6

The Pasted BMI & Birth weight Data

• BMI is coded as X since

it is the risk factor.

• Birth weight is coded as

Y since it is the outcome Y since it is the outcome

of interest.

• Risk factor first, then

Outcome.

• X comes first before Y.

• Capisce? (Understand?)

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Page 71: Introduction to Statistical Analysis Using Graphpad Prism 6

Pearson’s Correlation

• Click on “Analyze”, “XY

analysis”, then “Correlation”,

then OK again.

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• Tick “Compute r between two selected data sets”, “Yes, Pearson correlation coefficients”, then “Two-tailed”, then OK again.

Page 72: Introduction to Statistical Analysis Using Graphpad Prism 6

Correlation Results from Prism

• Prism states that there is a significant, positive & fair (r=0.4812) correlation between mothers’ BMI and babies’ birth weight. Therefore as BMI Therefore as BMI increases, the birth weight also increases.

• 23.15% (r2=0.2315) variability of the birth weight is determined by the variability of the mothers’ BMI.

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Page 73: Introduction to Statistical Analysis Using Graphpad Prism 6

3

4

5

Scatter Diagram - BMI vs Birth weight

weig

ht

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0 10 20 30 40 500

1

2

BMI

Bir

th

Page 74: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 6

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Page 75: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 6

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Page 76: Introduction to Statistical Analysis Using Graphpad Prism 6

Exercise 7

• 7. Conduct Simple Linear Regression using BIRTHWGT as the dependent variable. Try to come out with a formula that will predict the baby’s formula that will predict the baby’s birth weight based on the mother’s BMI. –y = a + bx

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Page 77: Introduction to Statistical Analysis Using Graphpad Prism 6

Simple Linear Regression

Qualitative

Dichotomus

Quantitative Normally distributed data Student's t Test

Qualitative

Polinomial

Quantitative Normally distributed data ANOVA

Quantitative Quantitative Repeated measurement of the

same individual & item (e.g.

Hb level before & after

treatment). Normally

distributed data

Paired t Test

Quantitative -

continous

Quantitative -

continous

Normally distributed data Pearson Correlation

& Linear

• mBMI and birth weight are both normally distributed

continuous data. Since the aim is to come out with a

regression formula between these two continuous

variable, therefore Simple Linear Regression is the

most appropriate test.

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continous continous & Linear

Regresssion

Page 78: Introduction to Statistical Analysis Using Graphpad Prism 6

Reuse BMI & Birth weight Data

• BMI is coded as X since

it is the risk factor.

• Birth weight is coded as

Y since it is the outcome Y since it is the outcome

of interest.

• Since the SLR uses the

same variables, we will

reuse the XY table from

Exercise 6.

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Page 79: Introduction to Statistical Analysis Using Graphpad Prism 6

Simple Linear Regression

• Click on “SLR” icon, it is just above the “Analyze” icon.

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• Just change the range so that the line will start at the y axis (X=0).

• We can set the line to end at the maximum value (it is X=41 in this exercise).

Click OK

Page 80: Introduction to Statistical Analysis Using Graphpad Prism 6

SLR Results from Prism

• Prism states that there is a

significant regression

coefficient (b=0.07323).

• The constant (a) is 1.081

• 23.15% (r2=0.2315)

variability of the birth variability of the birth

weight is determined by the

variability of the mothers’

BMI.

• BW = 1.081 + 0.073BMI

• For every increase of BMI of

1 unit, BW increases 0.07kg.

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Page 81: Introduction to Statistical Analysis Using Graphpad Prism 6

3

4

5

Scatter Diagram - BMI vs Birth weight

weig

ht

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0 10 20 30 40 500

1

2

BMI

Bir

th

Page 82: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 7

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Page 83: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 7

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Slight difference of the constant value. Prism calculated

1.081 instead of 1.079. Maybe it was due to decimal

difference of the BMI upon import.

Page 84: Introduction to Statistical Analysis Using Graphpad Prism 6

Question 7Question 7

drta

mil@

gm

ail.co

m

Birth weight

Page 85: Introduction to Statistical Analysis Using Graphpad Prism 6

The End

TQ to Dr. Sue-Mian Then for

challenging me to teach

Graphpad Prism 6.

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