Statistical and Critical Thinking

Summary

This video script emphasizes the importance of critical thinking in statistics, highlighting the need to complement textbook material with supplementary resources. It underscores the significance of active learning, such as writing definitions by hand and analyzing examples. The script warns against common pitfalls like confusing correlation with causation and the unreliability of self-reported data. It also addresses the impact of question order and phrasing on responses, the challenges of non-response and low response rates, and the potential bias in voluntary response samples. Additionally, it provides practical examples to illustrate the correct use of percentages and the distinction between statistical and practical significance.

Takeaways

• 📚 The video is a supplement to textbook material, not a replacement, emphasizing the importance of reading and understanding textbook content.
• ✍️ Writing out definitions and examples by hand is recommended for better memory retention and understanding.
• 🔍 Diagrams and charts should be copied by hand to help organize information and facilitate recall.
• 🧐 The video highlights potential pitfalls in statistical analysis, such as confusing correlation with causation.
• ⚠️ Correlation does not imply causation, a key concept to remember when interpreting statistical data.
• 🤔 The accuracy of self-reported data can be questionable, emphasizing the need for measured data over reported data.
• 🗳️ Loaded questions can lead to biased responses, so it's important to frame questions neutrally to avoid influencing outcomes.
• 🔄 The order of questions can impact responses, suggesting that the sequence in which options are presented matters.
• 🔒 Non-response and voluntary response samples can introduce bias, so it's crucial to consider who is responding and why.
• 📉 Low response rates can lead to unreliable data, so strategies to increase engagement and response are important.
• 🔢 Understanding the mechanics of percentages is crucial for accurate statistical analysis and interpretation.

Q & A

What is the primary purpose of the lecture videos mentioned in the transcript?

The lecture videos are supplementary to the textbook material, meant to highlight important concepts, provide examples, and clarify potential confusion points, rather than replacing the textbook.

Why is it recommended to write out definitions by hand when studying from a textbook?

Writing definitions by hand is believed to help the brain process and remember them more effectively.

What is a potential pitfall when dealing with correlation in statistics as discussed in the transcript?

A potential pitfall is confusing correlation with causation. The transcript emphasizes that correlation does not imply causation, meaning that two variables being correlated does not necessarily mean one causes the other.

How can the way a question is worded impact the responses in a survey?

The transcript points out that loaded questions, which are biased towards a certain answer, can sway responses. Additionally, the order in which options are presented can influence the choices people make.

What is a non-response in the context of a survey and why is it a concern?

A non-response occurs when respondents ignore a question or a survey altogether, which can introduce bias into the data by excluding certain perspectives and potentially skewing the results.

Why might self-selected samples in a survey be unreliable?

Self-selected samples can be unreliable because they are only from people who volunteer to respond, which may introduce bias if those who choose to respond have different characteristics than those who do not.

What strategies can be used to prevent low response rates in surveys?

To prevent low response rates, surveys should present an engaging argument for their importance, be quick and easy to complete, and potentially offer a reward for participation.

What is the difference between statistical significance and practical significance as outlined in the transcript?

Statistical significance is achieved when study results are unlikely to be due to random chance, often using a threshold of a 5% chance or less. Practical significance, on the other hand, refers to whether the findings make a meaningful enough difference to be considered useful or worth implementing.

How can percentages be misleading in statistical analysis as discussed in the transcript?

Percentages can be misleading if they are not accurately representing the actual data or if they are presented without context, such as not considering the total number of subjects in a study.

Why is it important to understand the mechanics of converting between fractions, decimals, and percentages in statistics?

Understanding these conversions is crucial for accurate data analysis and interpretation. It ensures that data is presented and understood correctly, avoiding misrepresentations that can lead to incorrect conclusions.

Outlines

00:00

📚 Textbook Study and Video Lectures

This paragraph emphasizes the importance of textbook study as a foundational step in learning statistical and critical thinking. It suggests writing out definitions by hand to aid memory, reading examples to reinforce understanding, and copying diagrams or charts to organize information. The role of video lectures is to supplement textbook material by highlighting key points and providing examples, rather than replacing the textbook. The paragraph also introduces the concept of pitfalls in statistics, such as the common mistake of confusing correlation with causation.

05:01

⚠️ Pitfalls in Data Analysis

The second paragraph delves into potential pitfalls in data analysis, particularly the misuse of correlation and causation. It uses the example of wet parking lots and rain to illustrate that correlation does not imply causation. The paragraph also warns against relying on self-reported data, which can be inaccurate, and stresses the importance of physical measurements for more reliable data. Additionally, it touches on the issue of loaded questions and the order of questions in surveys, which can influence respondents' answers.

10:05

🔍 Further Data Analysis Pitfalls

This paragraph continues the discussion on data analysis pitfalls, focusing on the dangers of non-response and voluntary response samples, which can introduce bias into the data. It also addresses the issue of low response rates and suggests strategies to prevent them, such as making surveys engaging, quick, and offering rewards for participation. The paragraph concludes with a warning about misleading percentages and the importance of understanding how percentages are used and calculated in statistical contexts.

15:06

👀 Observational Data and Bias

The fourth paragraph contrasts the reliability of observational data versus self-reported data, using the example of hand washing habits in public restrooms. It highlights the potential for bias in self-reported data due to social desirability and suggests that observing behavior directly can yield more accurate results. The paragraph also examines the potential for bias in research funding sources and the importance of considering the source of study funding when evaluating study outcomes.

20:08

📊 Statistical Significance vs. Practical Significance

This paragraph introduces the concepts of statistical significance and practical significance. It explains that statistical significance refers to the likelihood that study results are not due to chance, while practical significance pertains to whether the results are meaningful enough to be useful in real-world applications. The paragraph also discusses the importance of understanding the difference between these two types of significance and provides examples to illustrate the concepts.

25:08

🔢 Fractions, Decimals, and Percentages

The sixth paragraph focuses on the mathematical relationships between fractions, decimals, and percentages. It provides an example of converting a fraction to a decimal and then to a percentage, emphasizing the importance of understanding these conversions in statistical analysis. The paragraph also discusses the interpretation of percentages in the context of people or items, suggesting that results should be rounded to the nearest whole number when dealing with discrete entities.

❓ Suspicious Percentage Claims

The final paragraph addresses the potential for suspicious or incorrect percentage claims in research findings. It uses an example of a treatment's effectiveness in a small group to illustrate how percentages can be misused or misreported. The paragraph emphasizes the importance of understanding the mechanics of percentages to correctly interpret and question research findings.

Keywords

💡Statistical Thinking

Statistical thinking refers to the approach of analyzing and interpreting data using statistical methods. In the video, it's emphasized as a crucial skill for understanding patterns and making informed decisions. The video discusses how statistical thinking can help identify pitfalls in data analysis, such as confusing correlation with causation.

💡Correlation

Correlation is a statistical term that describes the degree to which two variables are linearly related. The video clarifies that a correlation between two variables does not imply that one causes the other, a common pitfall in interpreting statistical data. An example given is the correlation between wet parking lots and rain, where the wetness does not cause the rain.

💡Causation

Causation refers to a cause-and-effect relationship between events or variables. The video stresses that while correlation can suggest a connection, it does not prove causation. This is important in statistical analysis to avoid drawing incorrect conclusions about what causes what, as seen in the discussion about the relationship between sour cream consumption and motorcycle fatalities.

💡Pitfalls

Pitfalls in the context of the video are errors or difficulties that can arise in statistical analysis. The video outlines several pitfalls, such as confusing correlation with causation, relying on reported data versus measured data, and the influence of question wording on survey responses. These pitfalls highlight the need for careful consideration in data collection and interpretation.

💡Sample

A sample is a subset of a larger population that is studied to make inferences about the whole. The video explains the importance of understanding the difference between a sample and a population, and how samples should be representative to draw accurate conclusions. An example is given where 1048 adults are surveyed to infer about hand-washing habits among all adults.

💡Population

Population in statistics refers to the entire group that is the subject of a study. The video script uses the term to contrast with 'sample', indicating that while a sample is a smaller, manageable group, the population is the larger group that the sample is meant to represent. Understanding this concept is key to generalizing findings from a sample to a population.

💡Voluntary Response Sample

A voluntary response sample is a type of sample where participants choose to respond, potentially leading to biased results. The video warns about the unreliability of such samples because those who volunteer may have different characteristics than those who do not, thus skewing the data. An example is given where a survey posted on the USA Today website receives responses that may not be representative of all internet users.

💡Non-Response

Non-response refers to the absence of data from individuals who were supposed to participate in a study but did not. The video discusses how non-response can introduce bias into a study, as those who choose not to respond may differ systematically from those who do. It's a critical consideration in ensuring the representativeness and reliability of survey data.

💡Question Order Effect

The question order effect is a phenomenon where the way questions are ordered can influence the responses. The video provides an example where the order in which traffic and industry are mentioned in a question about air pollution affects which is seen as more contributing. This illustrates how the design of a survey can impact the results obtained.

💡Percentage

A percentage is a way of expressing a proportion or a rate per hundred. The video explains the importance of understanding percentages in the context of data interpretation, emphasizing the need for accuracy in calculations and reporting. The video also highlights potential issues with misleading percentages, such as a researcher claiming a treatment works in 53% of a group of 20 subjects, which mathematically does not add up.

Highlights

Videos serve as supplementary material to textbooks, not replacements.

Importance of reading textbook definitions and examples thoroughly.

Writing out diagrams and charts by hand to aid memory and understanding.

Videos help highlight textbook information and provide examples.

Analyzing data while avoiding pitfalls such as confusing correlation with causation.

Correlation does not imply causation, exemplified by wet parking lots and rain.

Physical evidence is required to justify causality, not just statistical analysis.

Potential inaccuracy in self-reported data versus measured data.

Loaded questions can lead to biased responses.

Order of questions can influence responses, as shown in traffic versus industry pollution example.

Non-response and voluntary response samples can introduce bias.

Low response rates can create bias and affect the usefulness of data.

Strategies to prevent low response rates include engaging surveys, brevity, and rewards.

Misleading percentages can occur if not properly understood or calculated.

Understanding the difference between statistical significance and practical significance.

The flaw in assuming causation from correlation, as seen in the sour cream and motorcycle fatalities example.

Converting fractions to decimals and percentages with examples.

Interpreting percentages in context, such as rounding to nearest whole numbers for people.

Suspicion raised by a researcher's claim of a treatment working in 53% of a small group.

Transcripts

this video is about statistical and

critical thinking and these lecture

videos are meant to be supplementary to

the textbook material and so they're not

meant to replace

anything you might be able to get from

the textbook but just go alongside it to

help highlight some important things

give some examples and so let's be

also very clear that the first step we

do in any section or topic should be to

read the textbook now that involves

probably a few steps that is write out

all definitions by hand

when you write them with your hand your

brain does better processing remembering

them

and then secondly we need to read all

the examples and note or write any

questions or points of confusion often a

textbook will have all kinds of examples

in them we should be reading them to

understand and reinforce the definitions

or topics being discussed

in the section and then thirdly write

out

that is copy by hand any diagrams or

charts often these can help organize

information and so we have to have those

written out so that our brain remembers

them and knows where we can go back and

find them

and so that's always a step we should do

so this this kind of like taking notes

from the textbook again is the

the main task in any topic or section

and then these videos will help

highlight some of the information in the

textbook

so then secondly let's talk about some

important highlights in this topic or

section

now we're going to talk about analyzing

data

and specifically some potential pitfalls

that could occur okay pitfalls are like

dangers right

and in the case of statistics

we have to be very careful about how we

handle certain things such as

correlation

and

causation

so specifically here correlation

does

not

imply causation

okay so first of all these are a lot of

fill in the blanks kind of definitions

and examples that you'll find in these

video notes and the the note guided or

templates that you can use to fill in

the blank should be available so you can

actually follow along and fill in

yourself

but they do

purpose to highlight and emphasize some

of these definitions now correlation

is different than causation as noted

here in this first potential pitfall for

example

wet parking lots may correlate

that is have a connection with rain but

they don't cause the rain right if you

drive by and see a parking lot that is

totally wet

it may be reasonable to conclude that it

rained recently and there may be other

clues that could help

you know inform that conclusion but

just because the parking lot's wet

doesn't mean the parking lot caused the

rain it simply goes with the fact that

it may have range right

and so we have to be careful not to

confuse these it's

in statistics often important to find

correlations or things that have

connections

but we can't jump too much from that

to some big you know causal conclusion

here that may or may not be true and so

as our author notes here secondly

statements about causality that is

what's causing something else can be

justified by physical evidence

but not by statistical analysis and so

we just have to be very careful not to

lean a little too far over our skis on

the statistical side and

take from a correlation which may

actually occur

and conclude from it some

specific causal relationship they may

not actually

be impliable

secondly

we also have to be careful

so first was that correlation does not

cause or does not imply causation

secondly

we could have a potential pitfall if

sample data is

reported

reported instead of

measured

okay so one example of this would be if

you're trying to do some kind of

statistical analysis that involves

getting

people's weights so let's say you know

the weights of everyone in a classroom

or everyone in a building or something

well if you simply ask people to report

their weight

as you can probably imagine we all kind

of want to look and sound a little

better than we actually are so you may

get inaccurate numbers

people may round down or round up

depending on the scenario right

whereas if you were to measure it such

as have an organized study where every

participant is like standing on a scale

the same scale and it's being measured

by a third party independent you know

person

looking at the weight on the scale you'd

end up with a much more accurate

set of of measurements or data

and then thirdly we also have to be

careful of what could be called

loaded questions

okay and loaded questions are

ones which give away or kind of lean

in a certain direction

and our author gives us a really good

example of one so there was a

set of questions given where the first

one said

should the president have the line item

veto to eliminate waste

now 97 percent of respondents said yes

okay but then when the question was

phrased should the president have the

line item veto or not

only 57 said yes

so notice the difference between the way

these two questions were asked the first

one went a little further it was loaded

with some extra information right should

the president have line item video veto

to eliminate waste

okay well you're you're loading the

question with a specific

purpose or application that may sway

people more than the initial part of the

question right maybe people say should

they see this question and think well

yeah of course we should eliminate waste

so i'm going to say yes to that whereas

the second question

simply said should the president have

line item veto or not that's a totally

different way of looking at that same

kind of question but it's not loaded

with any specific application and you

can see there's a difference in

responses right that to the second one

only 57 yes so so maybe that was getting

more at the responses pertaining to the

line item veto uh ability as as opposed

to the you know desire to eliminate

waste

and next we should discuss or consider

the order

of questions

that are provided

so again our author gives us another

example the first question reads

would you say that traffic contributes

more or less to air pollution than

industry

well in response to that question 45

percent blames traffic

and notice that was the first

possible factor mentioned in the

question

whereas

only 27 percent

blamed industry and that was the last

thing or second thing mentioned and so

the order in which things are mentioned

in a question has the potential to

impact the way people respond to them

or you'll notice in the second

instance of this

this time when the question was asked

would you say that industry contributes

more or less to air pollution than

traffic well notice this time

the order was reversed so this time

industry was was mentioned first

and then

traffic was mentioned second and guess

what the actual responses were reversed

this time

24 blame traffic 57 blamed industry and

so it could be the case in in this

scenario this example that the order of

the items mentioned the question

actually impacted the responses and so

you know we have to be clear when

gathering and working with data and we

want to just be aware for these pitfalls

that could give us totally different

outcomes and analyses simply based on

the way a question may be worded

next we have to consider

non-response

if we have respondents ignoring a

question or ignoring a survey

then it's quite possible

that having these non-responses may

already filter

the data by what types of people respond

or not right if people are less likely

even to respond then we're not gathering

or capturing

their authentic response and that may

influence

the overall results in a study or

a data gathering process

and secondly recall as in the textbook

here something called voluntary response

sample or self selected sample

can be unreliable or biased for the

exact same reason so a self

self-selected sample would be something

where you're getting

feedback and it could be authentic

feedback

but it's only feedback from people who

volunteered

to respond to the question well the very

fact that they may have volunteered

could have been influenced by some other

characteristic that's going to skew the

data or give it some bias so we have to

be very careful about non-responses

which is another way of saying voluntary

response sample as mentioned by our

author

next we should be aware or be careful

with

low

response

rates

so again if you're trying to gather data

from people and you're requiring some

kind of response to communicate that

if you have a very low response rate

um then that's a fair reason to to

wonder whether the the the information

gathered it's going to be useful or not

and so

as noted by our author this can create

bias in the results but to help prevent

low response rates there are a couple or

a few strategies

that could be used so um first of all we

could serve a survey should present an

engaging argument for its importance um

surveys are ignored more often than

they're embraced likely very likely

and so if we can get an engaging or you

know context or motivation for the

survey that can actually help a lot

or secondly a survey should should not

be very time consuming right quick and

easy is what people like and that's a

more likely to get a response

than if it's some you know 30 page

or even just three page survey we want

to be

conducive to people getting it done

quickly

or thirdly

it's helpful to provide a reward for

completing a survey and this is often

done in studies

where

sometimes respondents may even get paid

for their feedback it just depends on

the scenario but these are things to

keep in mind uh when we're trying to

gather data that low response rates can

cause problems so we should be careful

with them uh and by the way what is

actually low or not could depend on the

context and so those are all

also just considerations

that we'll be going over as we encounter

these

next we should consider

misleading percentages

misleading percentages now

the mechanics of percentages is not

something uh

taught exclusively in this class so

likely at this point you've already

worked with percentages we'll review

some of it

with some examples here shortly but

percentages are important now note that

a percent

really means divided by a hundred this

is just a strict mathematical definition

four percent we have to be careful that

that's how it's being used in any

statistical context

and secondly let's recall that

converting between decimals percentages

and fractions

is important sometimes we'll have to

actually do that in statistics

and we might want to make sure it's done

correctly

now let's spend a little time going over

some examples now these examples will go

with the content of this topic or

section and

some of it may you know touch on things

that weren't explicitly highlighted in

this video lecture so far there may have

been things from the textbook that

you've already been reading or taking

notes on and so this will help you know

give you some more to think about and

process in these topics all right so

this is coming from our author and

our first question says in a survey of

1048 adults conducted by bradley

corporation

subjects were asked how often they wash

their hands when using a public restroom

and seventy percent of the respondents

said always

okay so we want two parts here for part

a identify the sample and the population

with the definitions of sample and

population given in the textbook i

assume you've already written them out

by hand in your notes and you know

thought through some of the examples

printed in the book

but we want to understand these clearly

so a sample would be

a potentially smaller amount of people

than a population it doesn't have to be

smaller but it typically is smaller than

the larger or full

population a sample like you may imagine

if you go to a restaurant or something

and you sample some food you're just

getting a small portion of maybe what

they offer right

so let's identify in this case what the

sample and population are well in this

case a survey was given to

1046 adults so the sample

in this case would be 1046.

that's how many adults were surveyed

right

but the population

would be

all

adults

or you know you could say any adults

right well obviously there are a lot

more adults than 1046

so

the sample is in this case much smaller

but it's supposed to just get a smaller

representative

slice of what the overall population

may be or maybe like

and then secondly

with this question why would better

results be obtained by observing

the hand washing instead of asking about

it well this goes up to one of our

potential pitfalls we noted above which

is the the reporting as opposed to

measured

so when people report that they wash

their hands

there's probably an inclination to say

you did because it's it's probably a

little more noble looking or or

respectable looking to say you wash your

hands right and so that may sway the

results where people are maybe more

inclined

to to say they did just because it looks

or sounds better so

why would better results be given by

observing because reporting

results

can skew them as opposed to observing as

we noted above

secondly determine whether a given

source has potential to create bias in a

statistical study

in an article

in journal of nutrition okay so this is

a real publication here noted that

chocolate is rich in flavonoids

the article notes quote regular

consumption of foods rich in flavonoids

may reduce the risk of coronary heart

disease end quote

the study received funding from mars

incorporated the candy company and the

chocolate manufacturers association

okay so think about this for a second

right

do these candy companies have an

interest in people thinking that their

candy might actually be nutritious well

of course right that may

make people more inclined to buy and eat

it well if those people got if those

candy companies funded

this study

and the study made that conclusion that

these flavonoids found in their candy

may actually be good for you

there could be reason to wonder if

there's some bias in these results right

because it's it's more likely that they

wanted those results and they they

funded the study

thirdly let's determine whether the

sampling method appears to be sound or

is flawed

okay so first in a survey of

1368 subjects the following question was

posted on the usa today website in your

view are nuclear plants safe

end quote the survey subjects were

internet users who chose to respond to

the question posted on the electronic

edition of usa today

so we're trying to determine does this

seem to be appear to be sound or flawed

well

if you understand and kind of imagine

yourself in this context

these were people who chose to respond

right

to this electronic question posted in

this specific place this electronic

edition of usa today and so this is what

you would call self-reporting or

voluntary response sample

and so this could be dangerous and it

could cause biased results as noted in

our pitfalls above

or part b in a survey of social media

usage the pew research center randomly

selected 2002 adults in the united

states

well since it was randomly selected

this kind of construction of this sample

actually would be more or more reliable

we could say it appears to be sound

next let's describe the difference

between statistical significance and

practical

significance now to be clear we are

going to study statistical significance

in a more rigorous way and definition

later on in the course this is just an

introductory you know section on the

topic of understanding statistical

thinking so

the definitions provided in the textbook

which you should have written out and by

hand in your notes

do give just kind of a general sense of

it and so statistical significance is

achieved when a study produces results

that are unlikely to occur due to random

chance okay now that's the general

meaning of it a commonly used criterion

is that five percent chance or less of

random occurrence is acceptable again

this is going to be studied in more

depth later on but the point is

statistically significant has a

mathematical meaning to it

and it involves the results get uh given

in the study

not likely being just a chance like oh

we just flipped a coin and that's how it

ended up right it's more likely that it

was not chance it was due to some other

actual factor

now practical significance occurs when a

treatment or finding makes enough of a

difference to justify its use

so for example an arduous diet that only

sheds a couple of pounds may not be

practically significant to people right

and so you could say well this diet

showed that it had statistical

significance to reduce you know weight

in people they lost two pounds or

something well okay even if it's

statistically significant practically

significant means people actually care

about the result enough to try it so

want to make sure and understand the

difference between those two things

next let's identify what's wrong with

the following quote

in recent years there has been a strong

correlation between per capita

consumption of sour cream and the

numbers of motorcycle riders killed in

non-collision accidents therefore

consumption of sour cream causes

motorcycle fatalities

okay hopefully this one's jumping out at

you loud and clear if not you can go up

and review one of our pitfalls called

correlation does not

imply causation that was one of the

things we noted above

and in this case it's exactly what's

happening right there's a correlation

apparently between sour cream

consumption and these fatal motorcycle

accidents so okay what is the actual

cause of that well the statistics can't

really tell us

but what we can say is that

the correlation or association between

two variables does not mean that one of

the variables is the cause of the other

correlation does not imply causation

next let's talk about or review some

work with fractions and decimals and

percentages here so we have an example

that says convert

559 out of 1165

to the following forms

we want to write it as a fraction a

decimal and a percentage well as a

fraction we can take the phrase out of

and use that kind of like a fraction bar

and so if it says 559 out of 1165 we can

say

559

is the numerator

and then the

1165 is the denominator so out of

basically means over in a fraction set

up right

now we can convert this to a decimal

simply by using a fraction as division

right that's what a fraction means and

so we could take this fraction 559

over or out of 1165

and in a calculator perhaps write that

as 559 divided by

1165

now we weren't given any specific

instructions for rounding in this

example sometimes you may see actual

instructions for it and we're actually

going to talk about certain rounding

standards and conventions more as we go

on in later sections so since it wasn't

mentioned i'm going to just say for this

one let's round to 100

and the decimal point form when we

actually crunch this fraction in a

calculator

it's a long decimal but if we round it

to a hundredth uh so we'll say

approximately

since it's rounded

uh point or zero point

four

eight

if rounded to a hundredth

uh you could you know round it to

different values

just based on what was uh requested now

we convert a decimal to a percentage by

understanding decimal place values right

two places to the right of a decimal

which is where our value stops here is

called the hundredths place

well that's exactly what a percent

means is out of 100 and so 0.48 or 0.48

is the definition of 48

and so again this is a rounded decimal

and so i'm that consequently the

percentage would also be rounded um

but nonetheless these are how these two

or three definitions relate fractions

decimals and percentages of course you

can go back and forth or different

orders from one of the other depending

on what you're given and where you're

trying to go with it but this is how

they're connected

similarly for number seven the question

says how would we calculate and

interpret quote 48

of 342 people end quote

well we have to convert sometimes um

english to mathematics so when you say

48

of

342

that's like saying

the decimal form of 48 which is

0.48

of

342 could mean times

342. of in this context would be

multiply and so you could crunch these

two numbers

and the result that we could get after

just multiplying 0.48 times 342 on a

calculator would be

164.16

okay so now that was the calculate part

but then the next part said and

interpret well if you're talking about

people which is the context of this this

number here

you can't represent or reasonably

describe 0.16

of a person

0.16 so

rather we just round up to the nearest

whole number when we're talking about

people or you know items that can't be

divided up so obviously animals would be

something similar too but so in this

case you would describe it or interpret

as 164

people just rounding to the nearest

whole number

and then

lastly here what is suspicious about a

researcher suggesting a treatment works

in 53

of a group of 20 subjects

well the more we work with percentages

the more comfortable i think we'll get

with them but in this case when you're

talking about a

a set of 20 subjects

let's remember first of all for a

percent

a percent is defined by a part

over or out of

a hole so part out of the whole thing

right and you can actually crunch these

numbers out to get a percentage

a percentage for it so

in this case

there were 20 subjects which means the

whole

was 20. so if i have 20 as my

denominator

then the part would be you know how many

respondents out of 20 i'm trying to

represent well in this case

we're suggesting that for those you know

for whom this treatment works that would

be the part we're talking about here

we're suggesting that somehow the part

number out of 20

should equal 53 or perhaps rounded to it

but the point is

it would be roughly 0.53 right well if

we start messing around with some some

percentages if i had

10 out of 20

that would be zero point or just point

five

zero 0.5

or 0.50 you can always add a zero onto

the right without changing the number of

a decimal okay so point 50 that would be

50 that's close to our target of 53

percent but it's too low so let's go one

higher well the next higher would be if

it worked for 11 out of 20 uh subjects

right you can't have 10 and a half so go

to 11 out of 20. well it turns out

that's

0.55

so interestingly we skipped right over

the reported result of 53 percent and

we're suggesting that the numbers can't

even give you that result

you can get a 50 percent or 55 percent

but not this 53

given so that's reason to be a little

suspicious about where the

53 or the 0.53

came from you know were they rounding

something else what's going on with

these percentages so understanding the

mechanics of percents helps us use them

and

interpret them and be wary of them

correctly