The Manga Guide to Statistics

215 Pages·2016·89.7 MB·English

by  Takahashi Sh.

SHIN TAKAHASHI
TREND-PRO, CO., LTD.
TABLE OF CONTENTS

EEA Ee carapace era se vii
OUR PROLOGUE:

STATISTICS WITH # HEART-POUNDING EXCITEMENT @....0...0 0... wee All
1

DETERMINING DATA TYPES: cc2 129 cece sin ci eeteswsacens eh ence seweeweeuenra 13
1. Categorical Data and Numerical Data 2.0.2. 14
2. An Example of Tricky Categorical Data 22... 0. o cece cece eee e ees 20
3. How Multiple-Choice Answers Are Handled in Practice. ..... 0.000.000. c eee eee 28
Exercise and Answer... 2.6... ccc eee nec eect eve e ee ee eens 29
SUMMEID peters ie crt Otero te heer ret tren emi ine ore ian
Z

GETTING THE BIG PICTURE: UNDERSTANDING NUMERICAL DATA............ 31
1. Frequency Distribution Tables and Histograms .............0 02. ccevecevvsseeeeeeee 32
2, Mean (AVGTGE cs ccawawesemawwn cosine a9caew sean ae elMn swe N eS eRe eR ETE
CSAVCRE Terme eet cue RCC ee RTI ere ee err rte:

4. Standard Deviation. ................0.

5. The Range of Class of a Frequency Table

6. Estimation Theory and Descriptive Statistics ..........000 00 0c cece eee ee 57
Exercise and Answer Oe
SCMUIEIY 5 esa a eee eee Foo aCe ARES EC Ge HGH 6 wie sin wees eiwarenreiwleuewennues 58
3

GETTING THE BIG PICTURE: UNDERSTANDING CATEGORICAL DATA........... 59

1. Cross Tabulations
Exercise and Answer
SUMMALY as aos Bid eecem cieec ene ates

4

STANDARD SCORE AND DEVIATION SCORE... ec eee 65
1, Netmalizationvanid Standard! Sere va sya. gawa Vege Nig wa eS) AUS ee ey See kre p howe 66
2. Characteristics of Standard Score . 6.6.0.0. e eee e sees 73
$B Devise OMY SG NE) ac7 tr eccnerareraetiesiasac: blexeaeacced beesentier A acer ee oR oan eRe 74

S
LET'S OBTAIN THE PROBABILITY ©... cece eee neces 81
ae Prooanility. Dens PUnctio ly vena se wane eras euch aves ease hh eels Pe eee 82

2. Normal DIStiBUtlOty ie ¢xcewi’e fawn cam aenesiow verewe eum eae acuna wal epwies nace oma wane 86
3. Standard Normal Distribution ........ 0... cece eee ee 89

FETS G Ui ey car arn sneer ree yarns ame yw pera Ee A RIA Fg Nea mea a eg 95

[5-2 (yp) 0] ell | Ieee ee eee ceaty ema een Meni ere ta ny aiar Rita e RT Ee tech on et ie 97
Gs Chlaoqua he D ISth DUDS riemnw <aranensteeaya ws wiakansureeemeremena meen iwase eerie Se 99
Bitte (ist DUD Te iateus: anne rapt eiewe aa eras a RE Se SE
6. F Distribution :
PADish butions apie CXCE 1a ceases or ecene fs yt slew Sly eS eRe eee 107
HE SESH Go See ACLU NIE SOU cei ac ee eat gee ec ape 108
SUMMA cose es eae ee ee ee 109
6
LET'S LOOK AT THE RELATIONSHIP BETWEEN TWO VARIABLES .......... 111
AL, (Conrelation GOCHICIENE <oscannasse cmon ita vitesse mahi eese sarees sae eee See 116
Pine Gln afl eile) gu sclil¢ omer reaeee ener =4e claret coe career ine te net restr eciei cror nN cree ocr 121
OF Grea eles: @ oe titi ela tee eareee ees a eee een) 127
EXerciserand Answers cas reser aves bien ea indes Ge es eee aes Sees 138
SUPT TIN AD SY a5 ws Sea esa ae eS ed Oe 142
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LET'S EXPLORE THE HYPOTHESIS TESTS...... 2. ccc eee 143
TEAM M Se eenees Sire cere son estes rer eccenee cst ica meet ee teers Th
2. The Chi-Square Test of Independence. . .

Explanctions. pa. sais ete teeres es

EI Seapets ea ec aN Se ecm BT a

WB tel coh al sje key) =| calegemear nexus ent gle pemnsrs ts eer Ps peers 9 ay me er lebanon ges et Sue ener

ANSWEl' an 5 Wi Stren Ses BERETS See Eee Bee eae we ngs See Sel See SSE?
3. Null Hypotheses and Alternative Hypotheses ............... 0.00.2 c cece eee eee eee 170
4. P-value and Procedure for Hypothesis Tests.............. 0. ccccececeveeceeeeeeee 175
5. Tests of Independence and Tests of Homogeneity............0.....0 00 cee eee eee ee 184

Exarniple: ssassnew Ses neem eesseiemr ens mes oe we SGT wEs BES we Ny ows RRR TEES 184

PROCBUUTE ec aaasie di enaye reac e wale aan 2 wie eee 185
6. Hypothesis Test Conclusions. .........0 006 c cece eee ence ete eee e eee eens 187
Exercise anc ANEWel enete cee oer gens ore ct aS aera 188
SUGicl eee ate Teo Le Meee eer Th Terre ter ee cer ere eee 189
APPENDIX
LET'S CALCULATE USING EXCEL 6 cca cicca ve cevinvens ens duetuesius wuss 191
1. Making a Frequency Table .... 2.0.2.2. e cece teen eee eee ee 192
2. Calculating Arithmetic Mean, Median, and Standard Deviation....................... 195
@) Makiig) at Gross TabUaUGON eee tgs nem anton s er per ergy Eee Neve eychale SEES 197
4. Calculating the Standard Score and the Deviation Score............ 2... ccc eee eee 199
5. Calculating the Probability of the Standard Normal Distribution...................... 204
6. Calculating the Point on the Horizontal Axis of the Chi-Square Distribution............. 205
7. Caleulatirig the Correlation: Coetticietit os sys (a seers Kees ease eed omy ee 206
8» Performing) lests-oF Independence. cas gases tiie Sees ea cece em aves palate dea ead 208
Uy |b Ue Rec ie eames See TL ye re TC Renee ele Ree tele a Tee 213

Vi TABLE OF CONTENTS
PREFACE

This is an introductory book on statistics. The intended readers are:

* Those who need to conduct data analysis for research or business

* Those who do not necessarily need to conduct data analysis now but are interested in
getting an idea of what the world of statistics is like

* Those who have already acquired general knowledge of statistics and want to learn
more

Statistics is one of the areas of mathematics most closely related to everyday life and
business. Familiarizing yourself with statistics may come in handy in situations like:

* Estimating how many servings of fried noodles you can sell at a food stand you are
planning to set up during a school festival

* Estimating whether you will be able to pass a certification exam

* Comparing the probability that a sick person will get better between a case in which
medicine X is used and a case in which it is not used

This book consists of seven chapters. Basically, each chapter is organized in the follow-
ing sections:

* — Cartoon

* Text explanation to supplement the cartoon
* — Exercise and answer

* Summary

You can lear a lot by just reading the cartoon section, but deeper understanding and
knowledge will be acquired if you read the other sections as well.

| would be very pleased if you start feeling that statistics is fun and useful after reading
this book.

| would like to thank the staff in the development department of Ohmsha, Ltd., who
offered me the opportunity to write this book. | would also like to thank TREND-PRO,
Co., Ltd. for making my manuscript into a cartoon, the scenario writer, re_akino, and the
illustrator, Iroha Inoue. Last but not least, | would like to thank Dr. Sakaori Fumitake of the
College of Social Relations at Rikkyo University. He provided me with invaluable advice while
| was preparing the manuscript for this book.

SHIN TAKAHASHI
OUR PROLOGUE:
STATISTICS WITH
~ HEART-POUNDING EXCITEMENT @
2 OUR PROLOGUE

ey S\

THIS IS MR. IGARASHI. HE
WORKS FOR ME. I ASKED
HIM TO STOP BY BECAUSE
WE WERE HAVING A DRINK

TOGETHER NEAR HERE. ie ow
f\ joe

(Gz ii WELL, WELL.
WELCOME TO
OUR HOME ¢ SWEET
2
Q) () l=

y= Nl 2

S
I’M HOME, RUI!
SAY HELLO TO
MR. IGARASHI. HE
WORKS FOR ME.

YOU HAVE
A PRETTY
DAUGHTER.

MR. IGARASHI, WHAT KIND
OF WORK DO YOU DOP

YOU FLATTER ME!

BUT I DO NOT
DENY IT!

IN SHORT,
I DO MARKETING.

WELL, AS I WORK
FOR THE SAME
COMPANY AS
YOUR FATHER...

¥ STATISTICS WITH HEART-POUNDING EXCITEMENT » 3
TO EXPLAIN IT FULLY, I
DO MARKET RESEARCH
USING STATISTICS...BUT
I GUESS MARKETING |S
AN UNFAMILIAR WORD
FOR A HIGH SCHOOL
GIRL LIKE YOU.

YOU ARE HONEST! DO YOU
KNOW WHAT STATISTICS 15,

DID I MAKE
IT TOO
DIFFICULT?

OH, HERE
IS A GOOD
EXAMPLE!

SORRY, I HAVE NEVER

HEARD OF IT.

MAYBE YOU DON’T KNOW
THAT EITHER. ROUGHLY
SPEAKING, STATISTICS IS A
STUDY THAT ESTIMATES THE
STATUS OF A POPULATION
BY USING INFORMATION
GAINED FROM SAMPLES.

LOOK AT TODAY'S
PAPER.
HMMMM. NEITHER OF
YOU WERE SURVEYED,
BUT THE CABINET
APPROVAL RATING IS
IN THE PAPER.

Nun,
i
Hiatt
at

"ity

q
Way
gin

THAT'S WEIRD. YOU
TWO BOTH HAVE THE
RIGHT TO VOTE, DON’T
YOU?

IT SAYS THAT “ACCORDING
TO A CHOMAI TIMES
SURVEY, THE CABINET
APPROVAL RATING IS 39%.”

THAT'S MY POINT.
THAT'S WHERE
STATISTICS COMES IN.

CONTACTED BY THE CHOMAI
TIMES ABOUT THE CABINET.

I'VE NEVER BEEN

HOW ABOUT YOU,
MR. TAKATSUP

RUI, DO YOU
KNOW HOW
MANY VOTERS
THERE ARE IN
JAPAN?

LET ME
SEE...
ALOT!

(
I KNOW! @ (

¥ STATISTICS WITH HEART-POUNDING EXCITEMENT # 5&
RIGHT. YOU CAN GET
THE PRECISE CABINET
APPROVAL RATING IF
YOU SURVEY EVERY
SINGLE VOTER.

THAT IS WHY ONLY
A LIMITED NUMBER
OF PEOPLE ARE
SURVEYED.

SEE, RUIP THE REAL GROUP THAT SHOULD
BE SURVEYED IS CALLED A POPULATION.
A GROUP MADE OF SAMPLES SELECTED
FROM THE POPULATION IS CALLED A
SAMPLE. THOSE ARE STATISTICAL

& OUR PROLOGUE

HOWEVER, IT IS
UNREALISTIC TO SURVEY
EVERYONE. THERE ARE
TOO MANY PEOPLE.

DAD IS TORMENTING ME
BY TALKING ABOUT HARD