Evaluating Research Findings : Study with Video Lessons, Practice Problems & Examples

Descriptive Statistics – Measures of Central Tendency

This video, we're going to be going over descriptive statistics, which are basically stats that summarize your data. So, typically, when you get a new dataset, this is one of the first things that you're going to be looking at. And there are 2 main types of descriptive statistics. So we have measures of central tendency, which this video is going to focus on, and these basically tell you what values are the most typical in your data. And then we also have measures of variability, which basically tell you how much individual responses in your dataset vary, and we're going to cover that in an upcoming video.

So, to get into those measures of central tendency, we have 3 main measures: we have mean, median, and mode. So the mean is just the average value. Okay, and I'm sure many of you have calculated a mean, but just in case you haven't, you do this by adding up all the values in your dataset and then dividing by the number of values that you have. And we're going to practice finding each of these in just one second. Now the median is the middle value, okay, or the central value in your dataset and it's very easy to find.

All you have to do is put your values into numerical order and then find literally, like, the middle or central value within that dataset. And then the mode represents the most common or the most frequent value. Okay. So all you have to do to find your mode is just count how many times each value occurs, and the value that occurs the most times is the mode. So super easy.

We have a little dataset here of mock IQ scores. We have an n of 7, so we have 7 data points here. And I have gone ahead and just put these in numerical order so we can dive right into our calculations. And we're going to begin by finding the mean. So again, we're just going to add up all these numbers which for us would give us 735 and then we're going to divide by the number of, data points that we have which for us is again 7.

735 7 = 105

So 105 is the average number of this data set. Okay. Now, to find the median, again this is super simple, my favorite method is to just cross off the highest and lowest values and just keep working your way inward until you get to that central value. We're going to cross off the lowest and highest numbers, working our way in until we get to that middle value, which in our case is 95.

Now one thing to note is that this method does not work quite as well if you have an, an even number of data points. So, for example, if your data set was, like, 1, 2, 4, and 5. Obviously, you can't just tick these off because you end up with two numbers in the middle. What you would do in that case is basically just find the average of those two middle numbers. So you would do 2+4=6 divided by 2 equals 3 and so your median in this case would be 3.

2 + 4 2 = 3

So that's how you would calculate the median if you have an even number of data points. Alright, and then finally for the mode, again, super easy. We're just going to look at our dataset here and as you can see, every number occurs only one time except 85. So 85 is our mode because that number occurs twice. One thing to note is that if you have access to a graph of your data, like I have here, the mode is very easy to find because this will be basically where the graph peaks because there are multiple data points in that spot or more data points than anywhere else.

Okay. So if you have access to a graph, you can easily find the mode by just looking for the peak of that graph. Okay. One last note about each of these measures, a very important thing to be aware of, or the mean, is that the mean can be very easily skewed by outliers, which are basically just like unusual numbers in your dataset. So numbers that are much higher or much lower than every other value.

So, for example, in our dataset let's just say rather than 90 this was 200. Okay, as you can see 200 is quite a bit higher than all the other numbers, it's much higher than our next highest value of 135. In this case, 200 is an outlier. And what's going to happen is when you go to calculate the mean that really high number is going to artificially inflate the mean and make it look much bigger than it actually is. So it would no longer really be representing a true average of that dataset.

So if you have an outlier, whether it's higher or lower than your other values, your mean might not be quite as useful. Now luckily, we have the median and the median is a very useful measure to use if your dataset has outliers. And that is because the median is not dependent on the actual numerical values here, it's only dependent on its place within that dataset, so it's not going to get messed up by really high or really low values. And then finally, one note about the mode is that some datasets will actually have no mode at all. It is very possible to have a dataset, for example, where every number occurs only one time, and there is just no mode.

Likewise, you can also have multiple modes. So for example, let's say, you know, rather than 95, this was 90. In our case, we would have 2 modes. We would have a mode of 85, which occurs 2 times, and a mode of 90, also occurs 2 times. So mode can get kind of funky like that.

Don't be alarmed if you're not finding a mode or finding 2 or 3 modes. That can totally happen. Alright. So those are measures of central tendency, and I will see you guys in our next video. Bye-bye.

Evaluating Research Findings Example 1

Okay, so in this example, we're going to be calculating the mean, median, and mode of this dataset and then we're going to fill in the blanks of this statement here. So let's just start with the mean, median, and mode. Now the first thing that I did, if you have a small enough dataset, it's very useful to just write out all of your numbers in order. That's going to make it easier to calculate the median. But we're going to start by calculating the mean which is just adding up all of the numbers in our dataset and then dividing it by the number of data points that we have, which in our case is 7.

We have 7 data points here. So I'm going to add up all of our numbers which gets us 3,500,000 and then that divided by 7 is going to get us 500,000 for our mean. Alright. So that is our mean. Now our median is literally just our center value.

Right? And so to do that, you have to put your numbers in numerical order, which we already did, and then literally just find the value in the middle. So we're just going to tick off these numbers on either end until we get to the center value which is 325,000. Alright. So that's our median.

And then the mode is just the value that occurs the most often or the most frequently in our dataset. And in this dataset, every single number occurs one time except for 325,000, which occurs twice. And so that is going to be our mode. Alright. Now you may have noticed something here which is that the mean is quite a bit higher than the median and mode.

And that happened because we have this number here in our dataset which is significantly higher than the next highest value, which is only 425,000 which is nowhere near 1,500,000. Right? And so the mean really is not reflecting most of our data. If you look at these numbers here, you know, the mean does not look like the average of those numbers, does it? So in this case, we have an outlier in our data.

That 1,500,000 is an outlier and it's skewing the mean and really dragging it up and making it a lot higher than it really should be. So we're going to fill in the blanks of this statement and we're going to say in this dataset the mean is not as useful because it's been skewed by an outlier. And so in a dataset like this where you have one really clear outlier, the median is probably going to be your best bet when you're describing the data if you had to pick just one measure. In this case, the mean is really not describing the data in a very accurate way. Alright.

So that was our example and I'll see you guys in the next one. Bye bye.

Desmond is a graduate student who does a lot of work with household income data, and his samples almost always have outliers. Which measure of central tendency might be the most useful for Desmond to use?

• A. Mean.
• B. Median.
• C. Mode.
• D. Range.

Descriptive Statistics – Measures of Variability

In this video, we're going to be talking about those measures of variability. So, variability basically gives us a sense of how our data is spread out or how variable the data points are. And we use two main measures of variability in psychology: range and standard deviation. So range is basically just the difference between the highest and lowest values in the data. You literally just subtract the lowest value from the highest value, and that gets you your range.

It's very easy to calculate. Now with standard deviation, we're not going to learn how to actually calculate it. You don't really have to do that in intro psych, but just to give you a sense of what it is, it's basically going to be a value that indicates the average distance that each data point is from the mean. Again, just giving you a sense of how much your data is spread out. So, we are going to look at two different data sets and we're going to calculate some of our measures of central tendency and some of our measures of variability.

So, beginning with data set 1, this is a data set comprised of 9 values, and just looking at our graph visually, I can see that there's a fair amount of spread in this data set. There's some variability happening here. So, our mean has been calculated for us; our mean is 20, and we're going to go ahead and find the median just tick, tick, tick down to the middle. So let's find our median here, and it looks like our median is 20, the same as the mean. Alright, and then we're going to go ahead and calculate our range.

Again, we're just going to find our lowest value, which here is 0, and our highest value, which is 40. 40 - 0 of course is 40. So our range is 40. Pretty high range. So, we have a nice, very dispersive dataset here.

Now, because our dataset has so much spread and has so much dispersion, in a situation like this, you're probably going to have a higher standard deviation. Because again, when you're thinking about how the average distance of every data point is from the mean, well, if our means over here, we've got data way over here. Right? So we're going to have a higher standard deviation because we have so much more spread there. Alright, so looking over at dataset 2, again, this is made up of 9 values and just visually I can see that this dataset is much more clustered.

There's a lot less spread happening in this dataset, right? Once again, our mean has been calculated for us, and we are going to find our median. We'll find our middle value here, which once again, is 20. Okay, then we're going to go ahead and calculate our range. So here, our lowest value is 18, and our highest value is 22, so 22 - 18 would give us 4.

So now, we have a range of 4, much lower range as you can see. And again, because we can tell that this data has a lot less spread, in this case, we're going to have a much lower standard deviation for this type of dataset. Now, I made these data sets very specifically to prove a point. So you can see here that these data sets have the exact same means and the exact same medians. This is why it's very important to not only be considering those measures of central tendency but to also be looking at your measures of variability.

Because when we factor in these things, you get a really strong sense of how these datasets differ. But if you only have this information to look at, you might end up with a kind of skewed perception of what your data is looking like. So it's important to always be considering both your measures of central tendency as well as your measures of variability. They are telling you two very different and unique things about your dataset. Alright.

So those are measures of variability. See you guys in the next one. Bye bye.

Evaluating Research Findings Example 2

Okay, so here we have two datasets. We're going to be comparing them and choosing the answer that best describes the data, and all of our answers are basically just getting at which one of these has greater variability or if they have the same amount of variability. And we can calculate that very easily by looking at the range, which is very simple to calculate: just our highest value minus our lowest value. So in dataset 1, our highest value is 10 and our lowest value is 5, which would mean our range is going to be 5 for dataset 1 and in dataset 2 our highest value is 27 and our lowest value is 1, so our range is 26. This has a much higher range than dataset 1 has, which means that dataset 2 has greater variability.

There's just more difference, more variance, in those data points compared to dataset 1. So our answer here is going to be b. And there you have it.

Calculate the range of the following dataset: 22, 28, 31, 25, 42, 30.

• A. 17
• B. 20
• C. 12
• D. 14

Correlations

Everyone. In this video, we're going to be talking about correlations. It's very important to have at least a basic understanding of how correlations work because they're kind of the bread and butter of psychological research. We do a lot of correlational stats in psychology. A correlation is basically just a measure of the direction and strength of a relationship between two variables.

And we quantify them, turn them into a number using something called a correlation coefficient, also known as a Pearson's r. So if you see this little italicized r, you're typically looking at a correlation. We're going to go over what direction and strength mean separately. If we're talking about the direction of the relationship between two variables, what we're basically referring to is how these variables move in relation to each other. If we have a negative correlation, that means that our variables are moving in opposite directions.

So, for example, if our variables were parental sensitivity and children's anxiety symptoms. We might see that as parental sensitivity increases, children's anxiety symptoms decrease, indicating our variables are moving in opposite directions. That would give us a negative correlation. In contrast, we can have a positive correlation where our variables are moving in the same direction. For example, if our variables were parental sensitivity and children's well-being, those might be moving in the same direction, giving us a positive correlation.

It is important to remember that here, positive and negative do not mean good or bad. There's no moral value being assigned to these terms at all. You can have a positive correlation between, like, alcoholism and depression, for example. When we say positive or negative, all we are talking about is the direction of the relationship, basically just how these variables are moving in relation to each other. Okay.

So that is direction. Now we're going to move on to strength. If there is absolutely no correlation or no relationship between our variables at all, you are going to end up with an r of 0. Okay? Zero means that there is no relationship.

Now if we have an r of negative one or an r of positive one, those are what we call perfect correlations. An r of negative one is a perfect negative correlation and an r of positive one is a perfect positive correlation. You can see on these little charts, you can see how these data points are falling perfectly on those lines. It basically means that these variables are moving perfectly in sync with each other. That gives you a perfect correlation.

Now correlations of negative one and positive one almost never happen in real life in psychology research. So you can just think of them as the bookends on either side of our correlation spectrum here. No relationship, an r of 0.

A perfect relationship is going to be an r of positive one or negative one. When we're talking about the strength of a relationship, we're typically going to be describing our correlation as strong, moderate, or weak. These labels refer to the amount of dispersion in our data or how synchronized those variables are moving together. You can see here in our moderate graphs how we have a bit more spread in the data happening. They're clearly trending in the same direction, but they're not perfectly lined up on those red lines anymore.

Right? There's not so much synchrony. Whereas in these graphs that we have labeled weak, you can see there's quite a bit of distribution with these data points. They're really trending in the same direction but there's not a high level of synchrony there anymore. Now I'm sure you noticed that I did not put any numerical labels here, and that is because there is really no field-wide standard in psychology for what we consider a strong, moderate, or weak correlation.

This is going to differ among fields of psychology as well as different topics of study. And that's kind of annoying, but it just kind of is what it is. So if you begin to read psychological research and you notice inconsistent labels being used to describe the same correlation, you are not going crazy. There's just no standard. If I had to give you some numbers to kind of use as a jumping-off point, I would say often in psychology, correlations of 0.1 to 0.3 are typically described as weak.

Correlations of 0.3 to 0.5 are usually described as moderate, and then correlations that are higher than 0.5 are often described as strong. However, please don't take this as gospel. This is just kind of a starting-off point. Again, you will see different descriptors in different fields and among different areas of study. And I do want to be really clear, this applies to positive and negative correlations.

Okay? So the positive and negative sign is only telling you the direction of the relationship. The actual number is telling you the strength. Okay? So if we had a correlation of negative 6, that correlation is equally strong as a correlation of positive 6.

Okay? So these correlations would indicate that the variables are moving in different ways. Right? These variables are moving in opposite directions. These variables are moving in the same direction, but these correlations have an equal amount of strength.

Okay? Alright. So that is our little introduction to correlation, and I will see you guys in our next video. Bye bye.

Evaluating Research Findings Example 3

Alright, so Dr. Goldberg is examining the relationship between caffeine consumption and IQ. His data shows a correlation coefficient of r = 0.02 . Okay, so which of the following statements provides the best description of this data? So keep in mind with correlation coefficients, an r = 0 means that there is no relationship between the variables at all, and the strongest a correlation coefficient can be is 1, either -1 or +1. So, based on that, this correlation coefficient is extremely close to 0.

So close that we can fairly confidently say that there appears to be, based on this data, almost no relationship between caffeine consumption and IQ, and that would put our answer at b. Alright? So just keep in mind, obviously, we are not looking at a strong positive correlation in any sense of the word, and this is obviously a positive number, so we are not looking at a negative correlation. So that's why the other answers would be incorrect. So, our answer here is b.

Which of the following correlation coefficients indicates the strongest relationship between two variables?

• A. r = + .25
• B. r = + .55
• C. r = - .10
• D. r = - .65

Correlation Does Not Equal Causation

This video, we're going to be learning one of the most important phrases in all of psychology, correlation does not equal causation. What this phrase means is that if you are doing or interpreting correlational research, you cannot make causal claims about the variables. So you can't say this variable is causing this variable. All you can do with correlational research is describe the relationship that you are seeing between the variables. And there are two main reasons to keep this in mind.

So the first is that with correlational research there's going to be a lack, especially if it's cross-sectional, there's going to be a lack of temporal precedence. So basically, you just don't necessarily know which variable came first. And if you don't know which variable came first, you can't really say for sure which variable caused the other one. Right? That's just like basic logic.

The second reason is something known as the 3rd variable problem. So this is a situation where a correlation between 2 variables is actually being explained by a third variable. So, you know, again, correlational research is not like an experiment. In an experiment, you know, we're controlling everything that we can, we have equivalency between our groups, so the only variable that is different between the groups is going to be the IV. So the IV has to be theoretically what's causing the DV in a well-designed experiment.

But you don't have that level of control or manipulation in correlational research so there can be third variables that might be impacting your results. So to give you an example of this, we're gonna go over a real-life correlation that has caused some very alarmist reactions in real life. So some research has shown that playing violent video games is positively correlated with aggressive behavior in children. This has been replicated several times actually. So what we're seeing basically is that the number of hours, a, you know, child spends playing violent video games, we're seeing a positive correlation where we're seeing more aggression the more hours you spend playing video games.

Now a lot of this research has been cross-sectional, which means it lacks temporal precedence. So the research could be fine you know, theoretically could be finding evidence that playing violent video games is leading to aggressive behavior in children, but there is an equally likely chance that kids who were just more aggressive might be gravitating toward violent video games. Because we don't have the temporal precedence here, we can't really say which one of these is more true than the other one. Another thing that could be happening here is that third variable problem. So maybe, actually, kids who are exposed to more parental violence just happen to be more aggressive and play more violent video games.

Maybe kids who are exposed to more corporal punishment or physical discipline happen to be more aggressive and play more violent video games. Maybe kids who experience more peer rejection are more aggressive and play more violent video games. I could put like 30 different variables here and they would all work just fine. The point is with correlational research, you just don't know for sure and you just can't say definitively if these variables have a causal relationship. So you have to always be interpreting these things cautiously.

Now I want to be really, really clear. Correlational research is not bad. It is good research. It is absolutely necessary and important research in psychology. It's just important that you are interpreting it, in a way that is accurate.

So with correlational research, you can say that we are finding a relationship between variables. You can say that these variables are related in this way. You know, describe your correlation. Is it positive? Is it negative?

Is it strong? Is it weak? That is an accurate way to be talking about correlations, But you cannot take your correlational findings and ever say this variable caused this variable. That is reserved exclusively for experimental designs. Alright guys, so remember, correlation does not equal causation, and I will see you in our next video.

Bye bye.

Evaluating Research Findings Example 4

Okay. So Doctor Florence conducted a study and found that ice cream sales and crime are positively correlated. So we're going to write out 3 possible explanations for these findings and then state which one is the most likely. And this is a famous cautionary tale in psychology because this is a real correlation.

Ice cream sales and crime rates are actually positively correlated, and it is a fantastic example of why correlation does not equal causation. So our first explanation is that ice cream sales cause higher crime rates. Okay, ice cream sales cause more crime. How does that happen?

I don't know. It makes almost no sense. Right? Explanation number 2 is that crime rates lead to higher ice cream sales. So people are committing crime, they're super hungry, they're jacking up the ice cream sales.

Right? Also makes very little sense. And our third explanation is that there's actually a third variable at play here. So we have a third variable that's not being measured that is related to both ice cream sales and crime rates, for example, temperature. So when the temperature is higher, you tend to have higher ice cream sales.

You also tend to have higher crime rates because people are just out and about. People want to be outside and doing things. Right? Whereas in the wintertime or when the temperature is lower, you have lower ice cream sales and crime rates also decrease because people are staying in their homes. There's less opportunity to be outside.

It's less appealing to be outside. Right? And so in this case, this correlation is actually being driven by a third variable. And this is obviously the most likely explanation because these first two explanations don't really make any sense. And so this is a great fun little cautionary tale about why you cannot just look at a correlation and take it at face value and say, you know, this is telling us something meaningful because there's always a chance that there is a third variable at play especially when the correlation doesn't seem to make much sense in the first place.

Alright? So that is our little example and I will see you guys in the next one. Bye bye.

What does the third-variable problem refer to in correlational research?

• A. The presence of an unmeasured variable that may influence both variables being studied.
• B. When you examine more than three variables, correlational research becomes unreliable.
• C. The difficulty in determining if a correlation is positive or negative.
• D. A common error that can occur in correlational research when a sample size is too small.

Inferential Statistics

In this video, we're just going to briefly go over some inferential statistics. So, in psychology, inferential statistics are used to draw conclusions about how statistically reliable a study's results are. Essentially, we are asking, "Can we trust this data, and is the data from this sample truly representative of the population?" Inferential statistics basically show us the probability of getting the observed results, or just getting your results, if there had been no relationship between the variables in your study. Kind of a weird thing to think about, so I'm going to say that one more time.

But inferential statistics show us the probability or the odds of getting our results had there actually been no relationship between the variables in our study. Essentially what we're asking is, "What are the odds of this happening by chance? What are the odds that my results are a total fluke, basically?" And the field-wide standard that psychologists have agreed upon is that if the probability of the event happening by chance, or the probability of you getting these results by chance, is less than 5%, then we would consider your results to be statistically significant. So 5% is the agreed-upon threshold or kind of cutoff value that we use in psychology.

And to be clear, this is an arbitrary number. This was just decided on by people one day, but this is the field-wide standard as of right now. So we would write this out using something called a p-value, and the p just stands for probability. So if we're going with this 5%, then we would write this as p<0.05 and that would be considered a statistically significant finding. So you can see on our graph everything here on the left side in green, these are all indicative of significant p-values.

A p-value of 0.05 is significant, a p-value of 0.01 is significant, so this would indicate that there is basically a 1% chance of us getting these results completely by chance. A p-value of 0.001 is significant as well. And basically, what's happening is, the smaller this number gets, the more confident we can be in our results. As that probability gets smaller and smaller, we can really trust that these results probably do exist in the real world. You can see over here everything in gray would be indicative of non-significant p-values.

Okay, so if our p-value is greater than 0.05 that would be considered a non-significant result, or you could say like we did not find evidence of a statistically significant result in that case. Alright? So, basically, a big takeaway here when you go out to read research, make sure that you are seeing if a p-value is being described, always be on the lookout for those p-values being less than 0.05. Again and again, these are really common anchors that you'll see; 0.05, 0.01, and 0.001 are probably used most commonly in research.

So, just keep an eye out for these numbers and those would indicate that you are seeing statistically significant findings. Alright. That's our little introduction into inferential statistics. See you guys in the next one. Bye.

Evaluating Research Findings Example 5

Alright. So we're going to read through this example. We're going to be interpreting the results and then filling in the blanks here at the end. So the hypothesis here is that the new drug, pill XP, will be more effective at reducing anxiety and depression symptoms than a placebo will. And remember, a placebo is just a sugar pill.

Right? And so the experimental group, group A, takes pill XP for 1 week. Group B receives a placebo for 1 week. So group B is our control group here. And then data on anxiety and depression symptoms are collected at the end of the trial.

So our results are presented in a nice table here. We're looking at anxiety scores and depression scores. Remember group A is the experimental group and group B is the control group. So looking at anxiety scores, it looks like group A scored a mean of about 12 and group B scored a mean of about 26. So group B has a significantly higher score, than group A, and we can see that there was a significant \( p \)-value here.

So group A had a significantly lower anxiety score compared to group B. Then looking at the depression score, it looks like group A had a mean of 20 and group B had a mean of 21. Just visually those don't look very different and that is supported by our stats. It looks like there was a nonsignificant \( p \)-value here of 0.11. Alright?

So, if we're going to actually kind of write this out and interpret the findings, we could say something along the lines of group A had a statistically significant reduction in anxiety symptoms compared to group B. So just kind of looking at that again, we can see group A has a much lower anxiety score compared to group B. And then we would say the study did not find significant evidence with regard to depression scores. And, again, that language there is very important. We want to be saying things like we did not find evidence of a significant result or the result was nonsignificant.

That is the correct type of terminology to be using when we find a \( p \)-value above 0.05. Alright. So that is our little example, and I will see you guys in our next video. Bye bye.

Which of the following p values would indicate that a statistically significant relationship was found between two variables?

• A. p < .01
• B. p < .05
• C. p < .09
• D. Both a and b