Quantitative Data Analysis 101 Tutorial: Descriptive vs Inferential Statistics (With Examples)

In this video, we're going to jump into the often  confusing world of quantitative data analysis. We're going to explore what quantitative data  analysis is, some of the most popular analysis methods and how to choose the right methods for  your research. We'll also cover some useful tips, as well as common pitfalls to avoid when  you're undertaking quantitative analysis.

So grab a cup of coffee, grab a cup of tea,  whatever works for you and let's jump into it! Hey! Welcome to Grad Coach TV - where we demystify  and simplify the oftentimes intimidating world of academic research my name is Emma and today  we're going to unwrap the topic of quantitative data analysis if you're new here be sure to hit  that subscribe button for more videos covering all things research-related also if you're  looking for hands-on help with your research check out our one-on-one coaching services where  we help you through your dissertation thesis or research project step by step it's basically  like having a professor in your pocket whenever you need it so if that sounds interesting to you  you can learn more and book a free consultation with a friendly coach at www all right  with that out of the way let's jump into it quantitative data analysis is one of those things  that often strikes fear into students it's totally understandable quantitative analysis is a complex  topic full of daunting lingo like medians modes correlations and regression suddenly we're all  wishing we'd paid a little more attention in math class now the good news is that while quantitative  data analysis is a mammoth topic gaining a working understanding of the basics isn't that hard even  for those of us who avoid numbers and math at all costs in this video we'll break quantitative  analysis down into simple bite-sized chunks so you can get comfy with the core concepts  and approach your research with confidence so let's start with the most basic question what  exactly is quantitative data analysis despite being quite a mouthful quantitative data analysis  simply means analyzing data that's numbers based or data that can be easily converted into  numbers without losing any meaning for example category based variables like gender ethnicity  or native language can all be converted into numbers without losing meaning for example  english could equal one french could equal two and so on this contrasts against qualitative data  analysis where the focus is on words phrases and expressions that can't be reduced to numbers  if you're interested in learning about qualitative analysis we've got a video covering  that as well i'll include a link below so the next logical question is what is quantitative  analysis used for well quantitative analysis is generally used for three purposes first it's used  to measure differences between groups for example average height differences between different  groups of people second it's used to assess relationships between variables for example  the relationship between weather temperature and voter turnout and third it's used to test  hypotheses in a scientifically rigorous way for example a hypothesis about  the impact of a certain vaccine again this contrasts with qualitative analysis  which can be used to analyze people's perceptions and feelings about an event or situation in other  words things that can't be reduced to numbers so how does quantitative analysis work you ask  well since quantitative data analysis is all about analyzing numbers it's no surprise that it  involves statistics statistical analysis methods form the engine that powers quant analysis these  methods can vary from pretty basic calculations for example averages and medians to more  sophisticated analyses for example correlations and regressions sounds like a bunch of gibberish  don't worry we will explain all of that in this video importantly you don't need to be a  statistician or a math whiz to pull off a good quantitative analysis we'll break down  all the technical mumbo jumbo in this video so let's start by taking a look at the  two main branches of quantitative analysis as i mentioned quantitative analysis is powered  by statistical analysis methods there are two main branches of statistical methods that are used  descriptive statistics and inferential statistics in your research you might only use descriptive  statistics or you might use a mix of both depending on what you're trying to figure out in  other words depending on your research questions aims and objectives i'll explain how to  choose your methods later in this video so what are descriptive and inferential statistics  well before i can explain that we need to take a quick detour to explain some lingo to understand  the difference between these two branches of statistics you need to understand two  important words these words are population and sample first step population in statistics  the population is the entire group of people or animals or organizations or whatever that  you're interested in researching for example if you were interested in researching tesla  owners in the us then the population would be all tesla owners in the united states however  it's extremely unlikely that you're gonna be able to interview or survey every single tesla  owner in the u.

s realistically you'll only get access to a few hundred or maybe a few  thousand owners using an online survey this smaller group of accessible people whose  data you actually collect is called your sample so to recap the population is the entire group of  people you're interested in and the sample is the subset of that population that you can actually  get access to in other words the population is the full chocolate cake whereas the sample is just  a slice of that cake can you see what i've got on my mind anyhow why is this sample population thing  important well descriptive statistics focuses on describing the sample while inferential statistics  aim to make predictions about the population based on the findings within the sample in other  words we use one group of statistical methods descriptive statistics to investigate the slice  of cake and another group of methods inferential statistics to draw conclusions about the entire  cake and there i go with the cake analogy again but to be fair i always have chocolate on my  mind so with that out of the way let's take a closer look at each of these branches in more  detail starting with descriptive statistics descriptive statistics serve a simple but  critically important role in your research to describe your data set hence the name in other  words they help you understand the details of your sample unlike inferential statistics which  we'll get to later descriptive statistics don't aim to make inferences or predictions about the  entire population they're purely interested in the details of your specific sample when you're  writing up your analysis descriptive statistics are the first set of stats you'll cover before  moving on to inferential statistics but depending on your research objectives and research questions  they may be the only type of statistics that you use we'll explore that a little later so what kind  of statistics are usually covered in this section well some common statistical tests used in this  branch include the following the mean this is simply the mathematical average of a range of  numbers nothing too complicated here next is the median this is the midpoint in a range of numbers  when the numbers are all arranged in order if the data set makes up an odd number then the median  is the number right in the middle of the set if the data set makes up an even number then  the median is the midpoint between the two middle numbers next up is the mode this is simply  the most commonly repeated number in the data set then we have standard deviation this metric  indicates how dispersed a range of numbers is in other words how close all the numbers are  to the mean the average in cases where most of the numbers are quite close to the average  the standard deviation will be relatively low conversely in cases where the numbers are  scattered all over the place the standard deviation will be relatively high lastly we have  skewness as the name suggests skewness indicates how symmetrical a range of numbers is in other  words do they tend to cluster into a smooth bell curve shape in the middle of the graph this  is called a normal or parametric distribution or do they lean to the left or right this is  called a non-normal or non-parametric distribution okay are you feeling a bit confused  let's look at a practical example on the left hand side is the data set this data  set details the body weight in kilograms of a sample of 10 people on the right hand side we  have the descriptive statistics for this data set let's take a look at each of them first we can  see that the mean weight is 72. 4 kilograms in other words the average weight across the sample  is 72. 4 kilograms pretty straightforward next we can see that the median is very similar to the  mean the average this suggests that this data set has a reasonably symmetrical distribution in other  words a relatively smooth center distribution of weights clustered towards the center moving on to  the mode well there is no mode in this data set this is because each number presents itself only  once and so there cannot be a most common number if hypothetically there were two people who were  both 65 kilograms then the mode would be 65.

next up is the standard deviation 10. 6 indicates  that there's quite a wide spread of numbers we can see this quite easily by just looking at the  numbers which range from 55 to 90. this is quite a stretch from the mean of 72.

4 so we would expect  the standard deviation to be well above zero and lastly let's look at the skewness a result  of negative 0. 2 tells us that the data is very slightly negatively skewed in other words it has  a very slight lean this makes sense since the mean and the median are only slightly different as  you can see these descriptive statistics give us some useful insight into the data set of course  this is a very small data set only 10 records so we can't read into these statistics too much  but hopefully this example helps you understand how these statistics play out in reality also keep  in mind that this is not a list of all possible descriptive statistics just the most common  ones so at this point you might be wondering but why do these matter well while these  descriptive statistics are all fairly basic they're important for a few reasons firstly  they help you get both a macro and micro level view of your data they help you understand  both the big picture and the finer details secondly they help you spot potential errors in  the data for example if an average is way higher than you'd expect or responses to a question  are highly varied this can act as a warning sign that you need to double check the data and  lastly these descriptive statistics help inform which inferential statistical methods you can use  as those methods depend on the shape of the data we'll explore this a little bit more later  on simply put descriptive statistics are really important even though the  statistical methods used are pretty basic all too often at grad coach we see students  rushing past the descriptives in their eagerness to get to the more exciting inferential methods  and then landing up with some very flawed results don't be a sucker give your descriptive  statistics all the love and attention they deserve all right now that we've looked at  descriptive stats let's move on to the second branch of quantitative  analysis inferential statistics as i mentioned while descriptive statistics are  all about the details of your specific data set your sample inferential statistics aim to make  inferences about the population in other words you'll use inferential statistics to make  predictions about what you'd expect to find in the full population what kind of predictions  you ask well generally speaking there are two common types of predictions that research  try to make using inferential stats firstly predictions about differences between groups  for example height differences between children grouped by their favorite sport and secondly  relationships between variables for example the relationship between body weight and the  number of hours a week a person does yoga in other words inferential statistics when  done correctly allow you to connect the dots and make predictions about what you'd  expect to see in the real world population based on what you observe in your sample data  for this reason inferential statistics are used for hypothesis testing in other words to test  hypotheses that predict changes or differences of course when you're working with inferential  statistics the composition of your sample is really important in other words if your  sample doesn't accurately represent the population you're researching then your findings  won't necessarily be very useful for example if your population of interest is a mix of 50  male and 50 female but your sample is 80 male you can't make inferences about the population  based on your sample since it's not representative this area of statistics is called sampling but we  won't go down that rabbit hole here it's a deep one we'll save that for another video so what kind  of statistics are usually covered in this section well there are many many different statistical  analysis methods within the inferential branch and it would be impossible for us to discuss  them all here so we'll just take a look at some of the most common inferential statistical  methods so that you have a solid starting point first up are t-tests t-tests compare the  means the averages of two groups of data to assess whether they are different to a  statistically significant extent in other words to see whether they have significantly different  means standard deviations and skewness for example you might want to compare the mean blood pressure  between two groups of people one that has taken a new medication and one that hasn't to assess  whether they are significantly different simply looking at the two means  is not enough to draw a conclusion you need to assess whether the differences  are statistically significant and that's what t-tests allow you to do right next up is  anova anova stands for analysis of variance this test is similar to a t-test in that it  compares the means of various groups but anova allows you to analyze multiple groups not just  two so it's basically a t-test but on steroids next we have correlation analysis this type of  analysis assesses the relationship between two variables in other words if one variable increases  does the other variable also increase decrease or stay the same for example if the average  temperature goes up do average ice cream sales increase too we'd expect some sort of relationship  between these two variables intuitively but correlation analysis allows us to  measure that relationship scientifically lastly we have regression analysis regression  analysis is similar to correlation in that it assesses the relationship between variables but  it goes a step further to understand the cause and effect between variables not just whether they  move together in other words does the one variable actually cause the other one to move or do they  just happen to move together naturally thanks to another force just because two variables correlate  doesn't necessarily mean that one causes the other to make this all a little more tangible let's  take a look at an example of correlation in action here's a scatter plot demonstrating the  correlation or the relationship between weight and height intuitively we'd expect there to be some  sort of relationship between these two variables which is what we see in this scatter plot in other  words the results tend to cluster together in a diagonal line from bottom left to top right the  more tightly the results cluster together to form a line in any direction the more correlated they  are and therefore the stronger the relationship between the variables as i mentioned these are  just a handful of inferential methods there are many many more importantly each statistical  method has its own assumptions and limitations for example some methods only work with normally  distributed or parametric data while other methods are designed specifically for data that are  not normally distributed and that's exactly why descriptive statistics are so important they're  the first step to knowing which inferential methods you can and can't use of course this  all begs the question how do i choose the right quantitative analysis methods for my research  well that's exactly what we'll look at next now that we've looked at some of the most common  statistical methods used within quantitative analysis let's look at how you go about choosing  the right tool for the job to choose the right statistical methods for your research you need  to think about two important factors one the type of quantitative data you have specifically  level of measurement and the shape of the data and two your research questions and hypotheses  let's take a closer look at each of these the first thing you need to consider is the type of  data you've collected or the data you will collect by data types i'm referring to the four levels  of measurement namely nominal ordinal interval and ratio if you're not familiar with this lingo  you should hit the pause button real quick and go check out our post over on the grad coach blog  that explains each of these levels of measurement i'll include the link below okay so why does this  matter well because different statistical methods require different types of data this is one of the  assumptions i mentioned earlier every method has its assumptions regarding the type of data for  example some methods work with categorical data like yes or no type questions while others work  with numerical data like age weight or income if you try to use a statistical method that doesn't  support the data type you have your results will be largely meaningless so make sure you have a  clear understanding of what types of data you've collected or will collect once you have this you  can then check which statistical methods support your data types i'll include a link below the  video that explains which methods support which data types now if you haven't collected your data  yet you can of course reverse engineer the process and look at which statistical methods would  give you the most useful insights and then design your data collection strategy around this  to ensure that you collect the correct data types another important factor to  consider is the shape of your data specifically does it have a normal distribution  in other words is it a bell-shaped curve centered in the middle or is it  very skewed to the left or right again different statistical methods work for  different shapes of data some are designed for symmetrical data while others are designed  for skewed data this is another reminder of why descriptive statistics are so important since  they tell you all about the shape of your data the next thing you need to consider is your  specific research questions as well as your hypotheses if you have some the nature of your  research questions and research hypotheses will heavily influence which statistical  methods you should use if you're just interested in understanding the attributes of your  sample as opposed to the entire population then descriptive statistics might be all you need for  example if you just want to assess the means or averages and the medians or center points of  variables in a group of people descriptives will do the trick on the other hand if you aim  to understand differences between groups or relationships between variables and to  infer or predict outcomes in the population then you'll likely need both descriptive  statistics and inferential statistics so it's really important to get very  clear about your research aims and research questions as well as your hypotheses  before you start looking at which statistical methods to use never shoehorn a specific method  into your research just because you like it or have experience with it your choice of methods  must align with all the factors we've covered here all right now that we've looked  at what quantitative analysis is the two main branches of statistics and how  to choose the right methods for your research let's recap and bring it all together we've covered a lot in this video  well done on making it this far let's recap on the key points we've looked at  first we asked the question what is quantitative data analysis as we discussed quantitative  analysis is all about analyzing number based data which can include both categorical and numerical  data these data are analyzed using statistical methods the two main branches of statistics are  descriptive statistics and inferential statistics descriptives describe your sample the slice of  the cake while inferentials make predictions about what you'll find in the population the full  cake based on what you've observed in the sample as we saw common descriptive statistical  metrics include the mean the median the mode standard deviation and skewness on the inferential  side we looked at t tests anovas correlation analysis and regression analysis all of which can  help you make predictions about the population lastly we asked the important question how  do i choose the right statistical methods as we discussed to choose the right  statistical methods you need to consider the type of data you're working as well  as your research questions and hypotheses remember in this video we've only looked at a  handful of the most common quantitative methods there are many many more so be sure to check out  the grad coach blog as well as the other links below this video to get a fuller picture of what  all's on offer in terms of statistical methods also if you'd like us to cover any of the methods  in more detail be sure to leave a comment below alright that wraps it up for today if you  enjoyed the video hit that like button and leave a comment if you have any questions also  be sure to subscribe to the grad coach channel for more research related content lastly if you  need a helping hand with your research check out our private coaching service where we work with  you on a one-on-one basis chapter by chapter to help you craft a winning dissertation thesis or  research project if that sounds interesting to you book a free consultation with a friendly  coach at www www. bradcoach.