Normal Data Analysis with Software Part 1

Summary

In this tutorial, Matt demonstrates how to use statistical software, specifically StatKey and Statcato, to analyze normal quantitative data. Using a dataset of wrist circumferences from 40 women, he walks through the steps of importing data, calculating descriptive statistics like mean and standard deviation, and visualizing data through histograms and dot plots. The lesson emphasizes identifying normally distributed data, explaining the importance of the mean and standard deviation, and ensuring that the data is bell-shaped for accurate analysis. This video provides a hands-on guide for effective data analysis without manual calculations.

Takeaways

• 📊 The video introduces how to use software to analyze normal quantitative data, specifically focusing on using the mean and standard deviation.
• 💻 The speaker emphasizes the importance of using software to handle calculations, rather than doing them by hand.
• 📈 The dataset used for the analysis is health data, focusing on the wrist circumference of 40 randomly selected women, measured in inches.
• 🔢 The speaker demonstrates how to copy the data from an Excel file and paste it into analysis software for processing.
• 🖱️ StatKey is the first tool used to calculate the mean (5.067) and standard deviation (0.331) of the wrist circumference data.
• 📐 The importance of checking the shape of the data is highlighted, and a histogram is generated to confirm the data has a normal distribution.
• 📉 The speaker reduces the number of bins in the histogram to better visualize the normal distribution, which is bell-shaped with symmetry on both sides.
• 📊 A comparison between the mean and median is made to confirm that the data is not skewed, as they are close in value.
• 📋 The second software, Statcato, is introduced, and similar calculations (mean and standard deviation) are performed using the same data.
• 📏 The speaker explains that the mean plus or minus one standard deviation captures about 68% of the data, showing the typical range of wrist circumferences in this dataset.

Q & A

What type of data is being analyzed in the video?

The video analyzes normal quantitative data, specifically focusing on the wrist circumference of 40 randomly selected women, measured in inches.

Why is software used to calculate the mean and standard deviation?

Software is used to calculate the mean and standard deviation to avoid manual calculation errors and speed up the process, especially when working with large datasets.

What software tools are demonstrated in the video for data analysis?

The video demonstrates the use of two tools: StatKey and StatCato for calculating descriptive statistics like the mean and standard deviation, as well as creating histograms and dot plots.

How does the presenter suggest pasting data into StatKey?

The presenter suggests clicking 'Edit Data' in StatKey, deleting any existing data using Ctrl+A (or Command+A on a Mac), and then pasting the new data with Ctrl+V (or Command+V).

What steps are recommended for checking if data is normally distributed?

To check for normal distribution, the presenter recommends creating a dot plot or histogram in StatKey or StatCato, and adjusting the number of bars (or bins) to ensure the highest bar is in the middle and the tails are symmetric.

What does the mean and standard deviation represent in the context of this dataset?

The mean (5.067 inches) represents the average wrist circumference of the women in the sample, while the standard deviation (0.331) indicates the spread of the wrist circumference values around the mean.

Why is it important to assess the shape of the dataset before using the mean?

It is important to assess the shape of the dataset to ensure it is normally distributed, as the mean is only an accurate measure of central tendency when the data follows a normal or bell-shaped distribution.

What additional statistics can be calculated using StatCato?

In addition to the mean and standard deviation, StatCato can calculate other statistics like the minimum, maximum, median, and sample size (n).

What is the significance of the mean and median being close to each other?

When the mean and median are close to each other, it suggests that the data is symmetric and not skewed, indicating that the mean is a reliable measure of central tendency.

How does the video demonstrate calculating the range of typical values?

The video demonstrates calculating the range of typical values by adding and subtracting the standard deviation from the mean. This range (4.736 to 5.398 inches) represents the central 68% of the data, which is typical for normally distributed data.

Outlines

00:00

💻 Introduction to Analyzing Quantitative Data with Software

In this section, Matt introduces the topic of using software to analyze normal quantitative data, focusing on why it is more efficient to use computer programs rather than manual calculations. He provides an example using health data from his website, which includes various statistics like age, height, and wrist circumference for 40 men and 40 women. Matt walks through the process of selecting the 'women’s wrist circumference' data from an Excel file, copying it, and preparing it for analysis using statistical software tools like StatKey.

05:01

📊 Understanding Data Shape and Normality

Here, Matt explains the importance of knowing the shape of the data to determine if the mean and standard deviation can be used effectively. He discusses how to visually inspect the data's normality using histograms and dot plots. Matt demonstrates adjusting the number of histogram bins (called 'buckets' in StatKey) and explains how the highest bar in the middle and symmetry in the tails signify a normal, bell-shaped distribution, which justifies using the mean and standard deviation.

10:02

🔢 Calculating Basic Statistics with StatKey and StatCato

In this paragraph, Matt compares the use of StatKey and StatCato for calculating statistics like mean and standard deviation. He walks through how to paste the wrist circumference data into both tools, explaining how to manipulate columns and bins in StatCato. He reiterates that fewer bins (around three or five) are better for small data sets, and both tools show a normal data distribution. He highlights how the close proximity of the mean and median is a strong indicator of normality.

📐 Using Statistical Tools to Calculate and Interpret Data

Matt discusses the process of finding essential statistics, such as the mean, standard deviation, minimum, maximum, and sample size (n), using the statistics menu in StatCato. He demonstrates how these values are important for understanding the data, emphasizing how adding and subtracting the standard deviation from the mean can reveal 'typical values' that represent 68% of the data. Finally, he organizes the wrist data in ascending order and identifies typical values to further analyze the dataset visually.

Keywords

💡Quantitative Data

Quantitative data refers to data that can be measured numerically, such as heights, weights, and ages. In the video, the data analyzed includes the wrist circumferences of women, and the instructor uses this data to demonstrate statistical analysis using software. This concept is central to the video as it deals with how to process and analyze numeric information using mean, standard deviation, and other statistical measures.

💡Mean

The mean is the average of a set of numbers, calculated by summing all the values and dividing by the total count. In the video, the mean wrist circumference for the sampled women is calculated using statistical software. The mean is crucial because it provides a central value around which other data points are compared, helping determine the 'typical' wrist size in the sample.

💡Standard Deviation

Standard deviation measures the spread or variability of a dataset, indicating how much individual data points differ from the mean. In the video, the standard deviation for the wrist circumference data is 0.331, which shows how the wrist measurements vary around the mean. This concept is key to understanding the distribution of data and whether it is concentrated around the mean or more spread out.

💡Normal Distribution

A normal distribution is a bell-shaped curve where most data points are concentrated around the mean, with fewer points as you move away. In the video, the instructor demonstrates how to determine if the wrist circumference data follows a normal distribution using a histogram and dot plot. This concept is essential because many statistical methods, like using the mean and standard deviation, assume normality in the data.

💡Histogram

A histogram is a type of bar graph that represents the frequency of data points in different intervals (or 'bins'). In the video, the instructor uses a histogram to visually assess whether the wrist data is normally distributed. The number of bins in the histogram is adjusted to better fit the small sample size, showing how the shape of the distribution is revealed through graphical representation.

💡Dot Plot

A dot plot is a simple graphical representation where each data point is shown as a dot along a scale. In the video, a dot plot is used alongside the histogram to provide another visual way of assessing the distribution of the wrist circumference data. This helps to visually confirm whether the data is normal, with most dots clustering in the middle.

💡StatKey

StatKey is an online tool used to perform statistical calculations and create graphs, mentioned frequently in the video. The instructor uses StatKey to compute the mean and standard deviation and to generate visualizations like histograms for the wrist circumference data. This tool is central to the video as it performs the 'heavy lifting' of data analysis without requiring manual calculations.

💡Statcato

Statcato is another statistical software tool introduced in the video for conducting basic statistical analysis. The instructor demonstrates how to use Statcato to input data, create histograms, and compute basic descriptive statistics such as the mean and standard deviation. Statcato provides an alternative to StatKey, showing multiple ways of approaching the same problem with different software.

💡Descriptive Statistics

Descriptive statistics involve summarizing and organizing data using measures like mean, median, and standard deviation. In the video, the instructor uses descriptive statistics to summarize the wrist circumference data for the group of women. The goal is to provide a clear, concise summary of the dataset, helping to identify key features such as central tendency and variability.

💡Sample Size

Sample size refers to the number of data points in a dataset, which affects the reliability and accuracy of statistical results. In the video, the sample size consists of 40 women, and understanding this is critical when assessing whether the data is representative of a larger population. The sample size influences the interpretation of statistical measures, including how well the data fits a normal distribution.

Highlights

Introduction to using software for analyzing normal quantitative data.

Focus on not calculating mean and standard deviation by hand, but rather using computer programs.

Example data set used: health data from 40 women and 40 men, including age, height, and weight.

Specific analysis on women's wrist circumference data in inches.

Emphasized the importance of not altering raw data; advised copying data into new sheets for analysis.

Use of StatKey software to calculate the mean and standard deviation from pasted data.

Initial results: mean wrist circumference is 5.067 inches, and standard deviation is 0.331 inches.

Understanding data shape: importance of normal or bell-shaped distribution to validate the use of mean and standard deviation.

Visualizing data using histograms in StatKey to confirm a normal distribution.

Tips for adjusting histogram bars (bins) in StatKey to better represent small data sets.

Discussion on identifying normal distribution based on symmetrical histogram with the highest bar in the middle.

Comparison between mean and median to further assess data normality.

Use of Statcato software to visualize data and calculate descriptive statistics like mean, standard deviation, and sample size.

Explanation of how mean and standard deviation give typical data values and how to calculate these typical values.

Final data insights: values between 4.736 and 5.398 inches are considered typical for wrist circumference.

Transcripts

hi everyone this is Matt to show with

intro stats and today we're going to

look how to use software to analyze

normal quantitative data so we've kind

of seen the theory behind that we've

seen that we want to use the mean and

the standard deviation when the data

looks normal

but again we actually don't want to

calculate this stuff by hand we want to

actually have a computer program

calculate do the heavy lifting for us so

let's take a look at an example so this

again is my website Matt - to show our G

and we need some data so I'm going to go

to the statistics tab and I'm going to

click on data sets the data we're going

to look at today is the health data this

has here's the health data so I'm gonna

look here it's right here health data

I'm just gonna open the excel file so

health data Excel and you're gonna get

this one now this data actually has a

lot of data it has the random sample

data from 40 women and 40 men so it has

the data separated so you can see the

men's ages and heights and weights and

women's ages and Heights and weights and

things like that and it also has the

combined data so the combined data has

all 80 of the men and women so it does

have quite a beautiful day to set so

when you're looking for something just

keep kind of scrolling to the right

until you find what you're looking for

the data I'm going to look at today is

women's wrist circumference and infor in

inches so the they looked at they

measured how far around the wrist is for

these 40 randomly selected women in

inches okay

so again whenever you're working with

data like don't it's not as a good idea

don't mess up some raw data so I'm just

gonna copy this we learned last time

that if you want you hold your cursor

above the column so it turns into a

downward arrow and then just left-click

and it'll highlight the entire column

for you

and then push control-c or its command

see if you're in a mac and then we're

going to go ahead and paste that into a

new data set here so we have a new data

set here

there we go it's right there there's the

new data set yeah if I want to have the

computer calculate I'm going to use stat

Cato and stat key to calculate the mean

and standard deviation so we'll start

with we'll start with looking at stat

key so again you go to lock 5s com

that's where stat key is hosted you

don't need to save it it works so you

can just open it click on the stat key

button now this was one quantitative

data set so we're gonna click on one

quantitative variable it's under the

descriptive statistics and graphs sort

of on the top left it says one

quantitative variable so we click on

that now whenever you're pasting data

into something into a into stat key

usually you're gonna click the edit data

button so edit data now right now this

is kind of looks kind of weird you'll

notice you'll see the the numbers the

quantitative data but it also has a word

next to every number that sometimes

called an identifier these were how long

do certain animals live in years and

they were kind of showing what animal

that that number came from that's called

an identifier most of my data sets don't

have an identifier necessarily so so

what you're gonna do I'm gonna do is

just delete out this data again an easy

way to delete data out you can click and

drag it down if you want but I just like

push ctrl a ctrl a will highlight

everything even if you got a really huge

data set and then just push delete so

ctrl a delete

now I want to paste in the data that the

wrist data from the 40 randomly selected

women so I'm going to do that now if you

look this data does have a title so

titled means header row in stat in stat

key so you leave this checked it says

header row but it does not have an

identifier it doesn't have a word next

to every number so you want to uncheck

that one and then just push OK and there

we go

if you notice right away it calculated

there was 40 women that's the sample

size we see the mean was 5.0 six seven

we see the standard deviation is 0.33

one but again we have to know we we have

to know two what the shape of this data

set looks like for it to be for us to

know if we can use the mean and standard

deviation so what we said was it needed

to be normal or bell-shaped we can kind

of see from the dot plot that it does

sort of look sort of normal we got more

dots in the middle and as we get away

from the middle we have fewer and fewer

dots but it's better to look at the

histogram let's take a look at the

histogram now the the number of bars is

a lot for a data set is so small we only

have 40 women in this data set so having

10 bars or 10 bins or a stat key calls

it buckets so 10 buckets is a lot of a

lot of bars for this for this small of a

data set so I like to decrease the

amount of buckets you can kind of play

around with this a little bit and have

these go back and forth a little bit but

you can see right away that that looks

pretty normal right you can kind of see

how the data looks looks very normal and

also the mean which is the average 5.0

67 is pretty close to the highest bar

it's sort of right on the highest bar so

this is what we call normal or

bell-shaped the highest bar is in the

middle and the left tail is about

symmetric with the right tail all right

that's though you know normal when you

see it you can also decrease the number

of buckets if you want a number of bins

with this slider so here's here's five

bars or even three bars three bars works

pretty well

especially if the data is very very

small but this thing this data set

looked normal even at five bars or even

at seven bars so it looks pretty normal

we got we definitely have the highest

bar in the middle and it looks pretty

symmetric so we this is normal and what

we learned in our theory is that that's

when the only time the mean actually is

an accurate average so that we are

allowed to use the mean one thing to

take take a look at is that the mean and

the median are actually very close in

when we get to our discussions about

skewed data the the mean sort of gets

pulled in the direction of the skew but

if the mean and the median are actually

very close that's usually a good sign

that you're probably the mean is is

somewhat of an accurate average also

standard deviation is going to be our

spread for normal data okay so we know

the mean is five point zero six seven

and the standard deviation is 0.33 one

now I could have actually found this on

on statcato as well so whenever you're

copying and pasting in stat kado you

always want to make sure the title again

is in the gray so I'm gonna paste in

that data there it is women's wrists

data by the way you can pull these if

you put the cursor in between where it

says c1 and c2 you'll see it turns into

a sideways double arrow if you click you

can drag it open and see the title

better if you want okay so let's take a

look at our graph if we want to graph

this and see what the shape is I would

go graph and histogram all right there's

our histogram and then you just click on

the column that you want to make a graph

of this button down here this is show

legend is a good button it puts a title

on it for you so it's just kind of nice

I always like my graphs tab titles and

number of bins I know a stat key called

them buckets

yes but stat kado calls them bins and so

the number of bins 10 is quite a few I

think I'm gonna decrease this I think we

even like three bars would probably be

pretty well or

five or seven three usually works pretty

well if you have a small small data set

and we can see it does look normal right

the highest bar is definitely in the

middle so it looks looks pretty

symmetric okay and we can also have a

dot plot if we want it so graph and dot

plot and just click on that on the

column you want again show legend we'll

put a title and there's our dot plot so

you can kind of see even the dot plot

looks kind of normal

alright and now how do we find

statistics on stat kado well it's under

the statistics menu so you go to

statistics basic statistics descriptive

statistics

so again statistics basic statistics

descriptive statistics if you just want

to kind of calculate some basic

statistics for a quantitative data set

that's where you'd look again it will

ask you input variable that wants the

column so sometimes it'll have like a

you know you can click on the column but

this one doesn't so we have to type it

in c1 stands for column one so it's the

one that says here it's asking what

variable what column your data is in and

notice you have all kinds of different

statistics that they will calculate

here's a few that are I think are

important especially if you already know

that what I what I always do is find the

shape first and then identify which of

these statistics I want based on the

shape since we already know this data

was normal we're gonna want the mean and

the standard deviation so that they're

the meanest standard deviation right

there also it's nice to have the min and

the max I'd like to know the min and the

max cuz those might be outliers and I

also like to know how many numbers there

were so I like this button this is n

total if you remember the letter n

stands for sample size or how many

numbers are in your data set so those

when I have a normal data set these are

sort of the statistics I like to find

and I just pushed ok and there we go

it calculated it for us notice it got

the same really the same numbers that

stat key gave us the mean was 5.0 6 7

and the standard deviation is 0.33 one

the men was 4.2 max 5.8 and the end

total we had 40 women in the dataset

now what I want to show you though is

what are these numbers mean in terms of

the theory we learned last time so last

time we learned that if you add and

subtract the mean and the standard

deviation you get the typical values the

typical values so five point zero six

seven the mean minus 0.33 one the

standard deviation gives us four point

seven three six and the mean plus the

standard deviation gives us five point

three nine eight if you remember last

time where I mentioned that that's about

the middle 68% of the data now I just

want to kind of show you where that

sounds oh it's good to kind of have a

visual of the data now the one thing

about this is again this data is not in

order so what I'd like to do is just

kind of put it in order so I'm gonna

highlight this data set I'm gonna go to

home and right here you'll see sort sort

and I'm gonna sort smallest to largest

there we go and that just makes it

easier for me to kind of see this

visually so anything between four point

seven three six so four point seven

would be less so it has to be between

four point seven three six and five

point three nine eight are going to be

considered typical all right so this

would be considered typical all right so

there's our our four point eight