Statistics for Science

Hi. It’s Mr. Andersen and in
this video I’m going to talk about statistics for science. And the reason why statistics
is important in science is that’s what statistics is. It’s basically collecting, organizing,
analyzing, interpreting and then presenting data so that people can use it. And so we
don’t usually do a lot of statistics in high school science and that’s too bad because
it’s very important we understand what to do with data once we’ve collected it. And
there’s a big push right now to improve statistics knowledge of high school students. And the
reason why is that they become college students and they’re eventually going to have to start
working with what’s called Big Data. And so what it is Big Data? Well the days of a scientist
just lonely sitting by themself collecting data are gone. Most science now is done by
huge teams or groups or centers. And a lot of it is crowd sourced and we’re generating
so much data right now that we actually have to go through that. So what’s an example?
Well meteorology or the study of the weather and climate on our planet, we just get more
and more data, better data, but we have to pour through this to make models and make
predictions. Or genomics is sequencing of the genome. So looking at the actual letters
in the nucleotides in DNA and RNA. And we sequenced the human genome but now we’re sequencing
all these different organisms and so all that data is pouring in and we have to look through
it. Or this is a term I hadn’t even heard of before, connectomics, which is basically
using intense magnetic resonance imaging to look at neurons. Looking at the brain. And
then modeling that, using computers to model individual neurons and then grow that into
like a virtual brain. So you can see over the next 20 or 30 years we’re going to need
scientists who understand what to do with big data. And to understand big data, let’s
start by going through kind of the basics of statistics. And so when you’re dealing
with statistics, one big thing when we’re talking broad is the idea of what a population
is. And so a population is big. And so a population is going to be everything. So it could be
like all of the students in a class. So that could be a population. But it can get much
bigger than that. And so when we’re studying the population, not to be confused with like
a population that we study in ecology, the population, all of the characteristics of
that are going to be called parameters. And so an example of one that we’ll actually use
in science is N. That’s the population size. But I said that the population is everything.
And so it could also be like all of the stars in the universe. Or it could be all of the
planets in the universe. Or it could be not only one scientific experiment but an infinite
number of scientific experiments that you could do. And so it really is everything when
we’re talking about the population. And so if we go back to an example of a population,
well in science what we can do is take a sample of that. So this is the population and then
this is a sample of the population. And we move from population where we study parameters
and we get to the sample we have what are called statistics. And so statistics are going
to be characteristics of a sample. And hopefully that’s a random sample. And so a question,
a really good question at this point might be, which is more important? Is the population
important or is the sample important? In other words, which one do we use more? And I used
to think, you know, the population has to be the most important thing. We want to know
everything. We want to know all the outcomes. We want to know what the universe looks like
and in fact it’s the wrong answer. The right answer and the most important thing is the
sample, because you can never know everything, but you can know a sample of that. And if
you have a good understanding of the statistics we can make predictions about everything.
Predictions about the population. And so everything I’m going to talk about, I’m talking about
the sample because that’s what scientists do. We can’t do every conceivable experiment.
We can’t gather every conceivable piece of data. We just have to work with what’s called
the sample and make sense of that. So let me give you an example of thus. This right
here is, I remember reading there was a survey and they asked scientists like what’s the
greatest scientific discovery of the last 100 years. So from 1900-2000. And I thought
maybe it was going to be Einstein, relativity, or quantum physics or all of those things.
Actually the right answer, or the winner we’ll say was this guy. His name is Edwin Hubble.
And you’ve probably heard of his name because they named the Hubble space telescope after
him. But you might not know what he did. And so he sat here at the Mt. Wilson observatory
and he looked at galaxies in the universe. And what he found is that no matter where
he looked in the universe, they seemed to be shifted towards the red. So they were more
red in color. What does that tell us? Well, as objects move away from us, they get red-shifted.
And so it told him that all of these galaxies were moving away from us. In other words,
everything in the universe is moving away. And you can see that he just plotted that
in a nice little scatter plot and then we have a line of fit. And so did he measure
all of the galaxies in the universe? No. But he sampled, or he had a sample set of those.
And from that we can make predictions and what’s the prediction that we make based on
this? It’s the idea of an expanding universe. And the idea that all, since everything is
expanding that means everything was together at one point. And so this is that big bang
theory. That idea that all of the universe began at one singularity. And so let’s get
to some statistics. Let’s actually get to some numbers of the sample. And so let’s go
through these. The first one is going to be the sample size. That’s going to be the number
of observations that you make. So that could be the number in your sample group. In your
random sample. Next we have what’s called an X bar or the mean. The mean and the average
are going to be the exact same thing. So if you know what an average is and how to figure
it out, that’s going to be the mean. Next is the Median. Median is simply going to be
the midpoint in between all of our data sets. And then finally we have a range. And so this
is a sample set over here. So let’s say in the science lab this is some data that you
collect. And so could you figure out these four things: sample size, median, mean and
range? Well let me walk you through it. So the first thing we could do is the sample
size. And so sample size or n, get used to that letter n right here, sample size is just
going to be the number of samples that we made. And so in this set we have 1, 2, 3,
4, 5, 6, 7. And so our n value is going to be 7. Let’s go to the next one. What’s the
mean or what’s the average? Well to figure that out all you do is add up all of these
quantities and you’re going to divide it by the number of of quantities. And so if I add
all these up together I get 35. If I divide that by 7 which is the total number in my
sample size I’m going to get a mean or average of 5. How do you do the median? Or how do
you find the midpoint? Well, you have to line them up in order. So when I line it up in
order basically what I can do is I can cross it out from the sides. So I’ll cross one out
from the sides. I’ll cross another one out from the side and then we have the midpoint
which is right here. So the median and the mean in this case is going to equal 5. But
you might think to yourself, what do I do if it’s not even or if it is even? In other
words, what do I do here? Well I could knock off 2 from each side and let me knock off
another one from each side and now I have 5 and 6. So if this is our sample set, then
our median is going to be the average between 5 & 6 or the average is going to be 5.5 Let’s
get to the range then. What’s the range? The range is going to be the difference between
the extremes. And so this is the number 2 and this is the number 13. So this is my low
and this is my high, then my range is simply going to be 11 in this case. And so what are
these? These are all simple statistics that we can gather from a sample set. And again,
it’s a random sample from everything from this big population. Last thing I want to
leave you with is an idea that is sometimes is confusing to students and that’s called
degrees of freedom. And we refer to that as n minus 1. And so what is n? Well, n remember
is going to be the sample size and where does the freedom come from. Well I drew a, I drew
a flag right here to help you remember that. So what does it mean? What does a degree of
freedom? Well think of it like this. This is the best way to understand it. So imagine
I have these three numbers and they are going to add up to ten. And so this is A + B + C
equals 10. And I say choose a random number. And let’s make it easy by just choosing a
whole number. Well you might say that this is 3. And so I’m going to choose this to be
3. And did you notice I had total freedom? I had a freedom in my choice as to what number
I was going to choose to represent A. I had total freedom here. That was fun. Let me get
a little more freedom. So let’s say I’ve got to choose the next number B. I want to go
crazy. Maybe I want the next one to be 13. I could choose any number in the world. In
other words I have freedom to choose what that is. And so now this is fun. I have a
lot of freedom. So let’s go to the last one then. So we’re going to say that this plus
this plus this equals 10. So I’ve got a constraint here. It’s got to equal 10. Well now we’ve
got to choose C. Well what can C be? Well all of a sudden I’ve lost my freedom here.
In other words if this is 3, this is 13, this has to be negative 6 if I want this to be
10 because this is 16 minus 6. That’s got to be 10. And so all of a sudden I lost my
freedom. And so when we’re talking about degrees of freedom how do you figure that out? Well
you take the number in your data set, in this case it’s going to be 3 and you’re going to
subtract one from that. And so in this case I have 2 degrees of freedom of there were
two numbers at which I had a choice as to what I was going to choose. And so this will
be important in a couple of different ways. Number 1 when we’re figuring out standard
deviation using n minus 1 or degrees of freedom, we’re going to get more accurate results,
or more precise results. And so you’ll see this again when we calculate standard deviation.
And then when we start comparing data sets, when we do a Chi Squared test, it’s important
that you understand what a degree of freedom is. So if we have two different groups then
we’d only have 1 degree of freedom. Or if we have eight different groups or eight different
choices then we have seven degrees of freedom. And so those are all statistics. Again their
parts of the sample set which is part of everything and it allows us to give meaning to math.
And what I mean, I learned so much math in high school especially in algebra two, but
I didn’t always know like when am I going to use this? Statistics is something I promise
you that you are going to use. If you move on to college and hopefully get some kind
of advanced degree or find an awesome job, statistics will come back and it will find
you at some point so you might as well learn it now. So this is an intro on statistics
and I hope that was helpful.


  1. julian said:

    Cool! great work!

    December 1, 2012
  2. Richard Baker said:

    Good work again Paul. Your videos always help to de-mystify complex phenomenon.

    December 1, 2012
  3. rzxwm10 said:

    What is the purpose of a degree of freedom?

    December 1, 2012
  4. Bozeman Science said:

    It improves the precision of standard deviation and will become very important as we start to compare data sets using tests like chi-squared.

    December 1, 2012
  5. snakesandsticks said:

    When I'm looking to see if there is significant difference between two groups , I can use a chi-square, or a (1 or 2 tailed) t-test. I understand how to do them, but I'm not sure which to use depending on the circumstances. Any tips?

    BTW- I'm a graduate student in biology, and teach undergrad labs. Your videos are really help me prep for when I teach my students. Thanks!

    December 2, 2012
  6. Bilal Alshareef said:

    Hello teacher,
    I'm a medical student from Damascus University, and I would like to thank you for this video.
    Today we were taking a lecture in medical statistics, and our professor, were talking about the degrees of freedom, she confused us while she was talking, but I knew every she said, and my friends didn't, do you know why?
    Because I watched this video, you made the heard things simple and easy, esp. your example about the degrees of freedom, A + B + C = 10
    Thank you.
    I like your channel.

    December 3, 2012
  7. Emily Metzner said:

    What does it mean when people refer to 'overlap' in regard to standard deviation and/or standard error? Also, what are true means and sample means? Thank you very much!

    January 7, 2013
  8. Sofia Cardoso said:


    January 20, 2013
  9. IAmPiernik said:


    February 6, 2013
  10. maddienuts said:

    His video (including some other) helped me pass the CLEP Biology, Thanks

    February 23, 2013
  11. Safaa Az said:

    Great video as usual ! 🙂

    April 3, 2013
  12. Duleek Wadanamby said:

    Do you have a video for student's t test? if so can you give me the link please and if not can you make a video ASAP please???


    April 3, 2013
  13. Jack said:

    The degrees of freedom explanation was great, why didn't my college stats teacher explain it like that? He just said memorize this stuff and then tested us on it.

    April 3, 2013
  14. StephanieJayne7 said:

    Excellent, love the way you explained this. Thanks. Especially degrees of freedom.
    An ANOVA video would be wonderful

    April 17, 2013
  15. Rein Mellence said:

    Great explanation and video of course!

    April 27, 2013
  16. WTFbrownie said:

    even though i think statistics is one of the worst math classes (i love math like algebra and physics), you made seem clear about the concept of statistics.

    May 6, 2013
  17. GaborBartal said:

    Great videos, but sometimes odd – half the video is explaining that sample<population

    May 15, 2013
  18. Chrissie Eckersley said:

    can you do a video on ttests please. Thanks.

    September 18, 2013
  19. LPArabia said:

    Man I love you..SUBSCRIBE

    February 7, 2014
  20. daniel bishop said:

    Fast becoming my 'go-too-guy' for all my interests in science!  Keep it up, loads of us are loving it!

    March 14, 2014
  21. Jiwei Zhu said:

    best explanation of degree of freedom ever!

    May 10, 2014
  22. shuruq jaber said:

    best explanation ..Thank you 

    September 15, 2014
  23. momo2sxy4u said:

    I'm being forced to watch this .Thx alot 

    September 28, 2014
  24. Sam Sati said:

    Another brilliant and educating video. I thoroughly enjoyed it.

    October 3, 2014
  25. Won Seok Song said:

    10:55 it will find you. and IT WILL HUNT YOU DOWN AND KILL YOU

    October 26, 2014
  26. victory always said:

    I almost cried , because finally i know that i am not stupid , you clear most of the questions i had flying in my head with all this language and terminology of statistics language that i needed to understand , i just found your video and i,'ll watch all of them

    November 22, 2014
  27. TOOTHPAW said:

    great video

    February 12, 2015
  28. Carolina Gondra said:

    Great video!! Thanks for the explanation! 

    March 3, 2015
  29. SABELO MAKHUBO said:

    You good Mr anderson

    September 5, 2015
  30. YoY said:

    Yr teaching is amazing

    November 8, 2015
  31. Yassine oulad el majdoub said:

    thanks teacher, please can anyone guide me to a website where i can find some raw spreadsheets on biology surveys in order to practice some statistic tests

    November 28, 2015
  32. Hilmy Hilmy said:

    good clips. Don't stop making and continue with rest of stats topics… please

    September 4, 2016
  33. CjL716 said:

    You explain statistics clearly !!! Thank you …

    November 12, 2016
  34. Tyler Lake said:

    I enjected mariweed and I dieded

    February 15, 2017
  35. miaelisaromero said:

    This is awesome. Thanks so much.

    May 7, 2017
  36. Tianyi Xu said:

    First time knowing what degrees of freedom actually are.

    May 10, 2017
  37. Bryan Francisco said:

    this man is amazing. i learn a lot fro his videos. thanks sir

    May 21, 2017
  38. Franz Bardon said:

    pangu not new

    June 16, 2017
  39. ABINASH BEHERA Biology said:

    Why there is no video on null hypothesis???pls

    August 12, 2017
  40. Alaina Bell said:

    lol anyone here from AP Biology

    September 7, 2017
  41. Gerard Vignes said:

    I love you life sciences presentations. I didn't like your statistics presentations, and I have an idea why. It's not a good idea to combine concepts, computations and software in a single presentation, UNLESS you highlight one of these three and downplay the other two. For instance, emphasize the key concepts of probability and statistics that are critical to measurement data. You did this with mean, stdev and stderr. But downplay the math by only briefly showing/naming the formulas and avoiding the laborious crank-n-grind calculations. Also, downplay the software by showing excel, but already having all the data and macros set up and running properly. I like your good presentations, because you see (and describe) the forest, but you are also very knowledgeable about the trees (without getting lost in them). You are a great explainer of concepts, but then you show how those concepts are applied in practice. Many instructors are strong with crank-n-grind, but they don't do such a good job of linking the procedures to anything understandable or relevant. I prefer your approach, since you take the time to explain what the thing is and why it is important and how it gets used. I would also suggest that you avoid the mechanics of using software completely. Most students will learn to use Excel on their own (and from one another). Don't waste your time teaching that stuff. Also, to teach probability and statistics properly will require a LOT of videos. A lot of other people have already done that. Concentrate on applying statistics (and stderr) to scientific data.

    September 15, 2017
  42. Victoria said:

    Hii this is awesome! I'm taking Biology and I'm so confuseeee with all the date. Thank you so much for doing this.

    January 24, 2018
  43. D Capo said:

    My like statistic…. very mutch

    March 21, 2018
  44. Leumas Nowluck said:

    Really helpful.. thank u sir.

    March 22, 2018
  45. Mushtaque Ansari said:

    Great … Easy is better

    March 31, 2018
  46. Sam. A. said:

    Great explanation – thank you.

    May 17, 2018
  47. Aditya Patel said:

    Today's science is mainly focus on generating data…. Some time in some country it's only generating data not more than this.

    August 16, 2018
  48. Dentiste 110 said:

    Good videos. But please expand the statistics section more

    August 30, 2018
  49. Marcel Marceli said:

    Thanks a lot!

    September 1, 2018
  50. Yantsen YT said:


    September 17, 2018
  51. Yantsen YT said:


    September 17, 2018
  52. nadeem 999 said:

    Thank you so much

    December 6, 2018
  53. Jasmin Velasquez said:

    What is meant by objects get "red-shifted" as they move away?

    January 15, 2019
  54. Sajjad Ur Rehman said:

    Great brother

    May 18, 2019
  55. John Kinsey said:

    It’s lazy science. Statistics change over a population in a given location over a given time period. But big scientific consensus comes often, and it’s frequently from a study that was done from somewhere else other than the inquiry. You can’t have a scientific law that’s got a million variables that may change over miles or social classes or time periods, so basically anything. Even a basic group you could call normal people could cause a different outcome on 50% of outcomes of many experiments 10 years from then because knowledge and about 1000 other basic intelligence related categories change in such a short period of time. We are in such a great change in knowledge and teachings because of government pressure on education. People are getting so much more intelligent, even though they are taking more risks because you know, human, that I remember being so much more advanced than my parents in 11th grade at every possible subject. Able to analyze and see an easier and more probable outcome. Now at age 22, my brothers and sisters who are in 8th and 10th grade are doing things with math, science and literature that I didn’t fathom until my last year in high school or second year in college. The education is at such an uptick and science uses data to try to predict our future but you’d need an algorithm for an algorithm to actually achieve anything when you consider how fast our society is becoming an amazing behemoth of intelligent being. Like alien brainiacs from the movies. It’s amazing.

    June 6, 2019
  56. TheRunningGuy said:

    AP Bio Grind Time

    July 15, 2019
  57. SupahRookie said:

    5:35 all the important stuff was here, at least for my note packet.

    August 21, 2019

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