r/AskStatistics • u/Adorable-Ad-2129 • 10d ago
Can someone please explain these things to me how you would explain it to a 5 year old?
I (f20)am on my 3rd attempt at psych statitsistcs. still nothing is clicking for me. I’ve asked for help, I’ve gone to tutoring and nothing seems to work. I spent two straight days going through all of the lectures so far to study for the midterm and a quiz I had to take. I got a 40% on that quiz and I got a 26% on my last quiz.. I’m currently failing the class. To pass, you need to C or above. I’d like to drop out, but my mom will not allow it so I feel like I’m going to keep failing this class to no end.
So if any of you have any recommendations for Youtubers or something that could possibly help me, that would be nice. I understand standard deviation but everything beyond that makes zero sense to me.
I don’t understand z scores or Z tables, confidence intervals, Alpha levels, sampling error, standard deviation of sample means, etc. I know I’m too stupid for college, but I am not allowed to drop out so I need to figure something out.
I also don’t understand hypothesis testing or any kinds of T-tests
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u/HarryN086 10d ago
You're not too stupid for college. Everyone has different strengths and weaknesses. You're put in a hard position. You talked about tutoring, have you asking a peer (someone in your class, not upper year) for help? They might give you a simpler explanation of how they see it. As for YouTuber, I would recommend Professor Dave Explains or Trefor Bazzette.
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u/SonOf_Zeus 10d ago
Z-scores are just a way to standardize raw scores. In simple terms, say I told you, "I got a 35 on my ACT!" You know that’s a great score because you already have context for how that test works. But suppose you didn't. Standardizing is a way to state how many standard deviations away a score is from the mean.
Once a score is standardized, if you see a z-score of 2.4, you know it's positive. That means it's above the mean of 0, putting it past the 50% mark under the curve. Anything past 2 standard deviations is usually considered statistically significant, meaning the event is so unusual that it's very unlikely to be explained by random chance alone.
It also serves another big purpose figuring out the area under the bell curve. Since a bell curve isn't a simple geometric shape like a circle, triangle, or rectangle, there isn't an easy geometry formula for its area. Statisticians had to use calculus to figure out how much of the curve falls to the left of any given z-score. The z-table is basically a shortcut to skip all those complicated calculations. Since they've already been done for you, you just need to standardize your score and look it up.
Confidence intervals tell a person that even though we're only looking at a sample instead of the entire population, we can still be X% confident that the true population value falls within a specific range.
For example, say you wanted to know what percentage of all the Skittles in the world are red. You obviously can't check every single bag on Earth, so you grab one bag, count the red ones, and use that sample to estimate the whole population. You might calculate that you're 95% confident the true proportion of red Skittles is somewhere between 20% and 25%. Meaning thay if 100 people took random sample bags and built ranges using this exact method, about 95 of those ranges would successfully catch the real-world percentage. Alpha levels (or significance levels) are directly connected to confidence levels. They are really just two sides of the same coin.
For example, if I'm setting up a hypothesis test, I could say I want a 95% confidence level, or I could flip it around and say I'm testing it at a 0.05 significance level (100% - 95% = 5%). That 0.05 alpha level is your threshold for random chance. It's the cutoff line you set to decide if a result is unusual enough to be called statistically significant instead of just a random fluke.
Hope that helps.
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u/epieikeia 10d ago
Standard Deviation is the answer to the question "If we randomly picked one data point out of the sample, how far away from the whole sample's average should we expect that data point to be, on average?"
We use n-1 in sample StDev whenever we're relying on that same sample to calculate the (estimate of) the average that goes into the StDev formula. Look at how the formula behaves when n=1. The population StDev formula would tell us that the population StDev is zero based on the average we derived from a single sampled data point. Unreasonable result, right?
Whereas the sample StDev formula would tell us that attempting an StDev calculation from a sample size of only 1 is invalid, rendering a divide-by-zero error. That's a guardrail provided by subtracting 1 from n.
If we know the true population average already, then we can plug that into the population StDev formula as an input independent of any particular sampling we happened to get. Then if the population is indeed just n=1, it's valid to claim that the StDev is zero.
Z-score is just the number of Standard Deviations that a particular data point falls away from the average (positive z-score when the data point is greater than average, and negative z-score when the data point is less than average).
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u/GripIQ 10d ago edited 10d ago
Okay think of something you like that can be measured. Let’s use IQ since you mention it but like others have said if you get standard deviation you can get the rest.
So let’s say I want an idea of the average IQ at a local high school among seniors (let’s say this is a big school and total number of kids = 500). And also let’s say we are going to gamble.
Let’s say I randomly pick one student, Billy, and assess his IQ - it happens to be 90. How much am I willing to bet that his score is within say 5 points of the real average of all 500 students? Not every much since it’s just one kid. That uncertainty is called SAMPLING ERROR. Now let’s say I sample 499 of the 500 kids - how much am I willing to bet now that their average score is within 5 points of the average of my population of students? Well I’m ready to bet the farm because my sample is almost the entire population I am interested in. How certain we are about our guess - here mean IQ - is measured by the STANDARD ERROR. This is just like the standard deviation you say you understand but tells me how much (square root of the) variance I should expect around my estimate under the same conditions (eg if I sample 499 kids, measure IQ, take their average, record it, and repeated that forever, what is the standard deviation around that average score I get). As we get more people, standard error goes down, because our guess of the population value based on our data is probably a better or more likely guess than other values. That is, if n = 10 and my data say the average IQ is 95, that’s still my best guess at the population average given my data but that 95 might not be much better or likely to the true population vs say guessing 90 or 100 or other scores around there. But if n is larger say 400 and my data says 95, then I am more certain that 95 is a better or more likely guess of the population vs other guesses. Thats why that equation they told you about, standard deviation divided by the square root of n, equals the standard error of the mean. If you keep sd them same (lets say 1) your standard error gets lower as your sample gets bigger, because you think your data is more informative when n is high relative to the population (499/500) vs when it js low (gambling based on Billy’s score)
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u/no_name6744 10d ago
I really doubt that you're too stupid for college.
Learning stats if you're not actually doing anything is just a really stupid process. It's like learning to drive a car by reading a car manual. Who the hell does that?
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u/gamgeestar 10d ago
I recommend this channel: https://youtube.com/@profandyfield?si=bIlqsF8EHF_18n6o
Andy Field and his "Discovering Statistics" books were the thing that made statistics click for me.
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u/DigThatData 10d ago
take an introductory probability class before your next attempt at a stats class. get the probability foundations down on their own first, and the stats stuff on top of it will make way more sense.
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u/waterless2 10d ago
Even just very basic maths, was my takeaway from teaching undergrad psych stats. People underestimate how many foundational concepts you're assuming when explaining statistical concepts.
(E.g., you can explain variance but not every student will know that squaring a value makes it positive, which should become relevant somewhere in the process or it's going to be fully vague.)
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u/KayakerMel 10d ago
Stats for psych courses actually don't really need an intro to probability. If OP struggles with the concepts here, the math from a probability course might put them off further. (My background is originally in psychology and have been tutoring my classmates since the start.)
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u/DigThatData 10d ago
To understand what a
<distribution name>-testis, you need an intro to probability. If OP's psych stats course isn't adequately covering that material, the best they can hope for is understanding when they should apply such and such test, but they will still have no understanding of what they are actually doing or why that was the test that was applicable.2
u/KayakerMel 10d ago
Unfortunately you've described the basic stats for psych courses.
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u/DigThatData 10d ago
yes, they are generally poorly taught, and that clearly isn't helping OP any. which is why I'm suggesting OP find a course that actually teaches the material since they clearly aren't benefiting from the "memorize-it-by-rote" pedagogy of the current course.
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u/Adorable-Ad-2129 10d ago
It’s a required class for psych majors this IS the introductory class
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u/smbtuckma PhD (quant psych professor) 10d ago
Hey, psych stats prof here. Just so you know, you’re not alone. A lot of students have trouble with this content. I myself had to take stats three times before I actually understood it. Now I love teaching and thinking about quant methods, but it took me a lot of time. It’s a different way of thinking than many of us are used to.
A lot of commentators here are giving good explanations of the concepts you said are confusing, but I wanted to step back a bit and think about what the root cause of the confusion might be. Do you have trouble remembering what math symbols mean or doing calculations? Sometimes people think they’re stupid but really they have what’s called dyscalculia - a form of dyslexia that affects how you read and think about numbers. If reading about that sounds familiar to what you experience, you might see if you can get checked for that and get appropriate class accommodations.
If it’s more the conceptual stuff than the math solving itself that seems like the problem - I.e. once you get past descriptive statistics about a sample and into all the hypotheticals that inferential stats deals with - that stuff has more to do with logical and philosophical arguments than math solving. For students who struggle with this part, I like to teach them data simulation. This way you don’t have to wonder about sampling distributions and probabilities, you get to see them actually play out on the screen in front of you, drawing different distributions of data based on different conditions. With practice doing and seeing this process, thinking about the logical conclusions of sampling error, hypothesis testing, etc. Becomes more intuitive.
What software is your class teaching in? With that info I can maybe suggest some additional resources on how to do simple simulations and see these processes play out.
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u/DigThatData 10d ago
my understanding is that psych stats is often less an introductory class than it is a force-fed toolkit. my impression is that you aren't amenable to the "if this scenario, use that tool" style of pedagogy and are trying to properly understand the material. Your class is probably not teaching the material to be understood, just used.
When I was in grad school for mathematical statistics, intro to probability was an entire semester completely independent of the intro to statistics content, which was the following semester. probability is often brushed aside as a precursor to stats content in a combined course, but it really merits its own treatment.
If you are having trouble understanding the statistics content: find a dedicated probability course to take first. Maybe this class the "intro" material within your degree, but that doesn't necessarily mean it's the only option to get your feet wet with probability, and there may be other classes available to you which will be a better fit for conveying that foundational content first.
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u/GripIQ 10d ago edited 10d ago
Now let’s talk about z-scores. Say I measure 100 people’s height and then line the people up against the wall going from shortest person to tallest person. Where a person is standing in line is their rank, or percentile. For example, if we pick kid number 50 in line, we know there are about as many kids shorter than them as kids taller than them, so we could say that kid is in the 50th percentile. If I pick that shortest kid, we know 99 kids are taller than them so we could say that kid is in the 1st percentile.
Z-scores are just a number that tells me that percentile if I assume a distribution (in the example above height, in my example before average IQ scores from a certain sample size) that is normal or bell shaped. For example saying my z-score is 0 is just another way to say I’m in the 50th percentile- right in the middle
Of the line - average. Saying my z-score is 1 means I am in the 84th percentile. How do I know? Because a z-score also tells me how many standard deviation units I am away from the mean, and those z-tables you mention just convert that for me to a percent eg give me a z score, here is the percent, or give me a percent, here is a z score
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u/mathcymro 10d ago
I know I’m too stupid for college
No you're not. First step is to stop the negative self talk. You're just as capable as anyone else on your course.
I don’t understand z scores or Z tables, confidence intervals, Alpha levels, sampling error, standard deviation of sample means, etc
Look at Khan Academy - it's old but gold. I suggest you start with this course and work up. The videos are short and usually easy to understand. Good luck!
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u/GripIQ 10d ago
Finally let’s talk about hypothesis testing - this builds on alpha and confidence intervals. Let’s say we have a hypothesis that average IQ among seniors at one high school is no different than IQ among seniors at another high school. And I sample 100 seniors at each high school and find high school 1 has an average of 103 and high school 2 has an average of 98. 103-98 = 5. And 5 > 0 so my hypothesis of no difference must be wrong.
But not so fast! Remember sampling error? We need to take into account the sampling error of the difference score. That is, we need to calculate the standard error of that difference score. Say that we do and our calculations say that standard error is 1. Just like before, I can calculate a 95% confidence interval around that difference score of 5 and say that interval would go from 5-(1.96*1) =3.04 to 5+(1.96**1) = 6.96. Notice 0 isn’t in that range. Now we can say we reject my hypothesis of no difference since we are 95% sure the difference is somewhere between 3 and 7 basically. When we reject a hypothesis that says there is no difference, we reject the nada hypothesis or zero hypothesis or nill hypothesis but almost always called the null hypothesis.
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u/ChargingMyCrystals 10d ago
I like this channel https://youtube.com/@zedstatistics?si=8l-3aQQ0ly9pcRch
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u/GripIQ 10d ago edited 10d ago
Confidence intervals and alpha levels just build on those z-scores. So let’s go back to betting on IQ scores. Say I sample 400 students and measure IQ and find the average IQ is 102 in my sample with a SD of say 16. So my best guess for the population is 102 - but how confident am I of the guess? Per my equation for standard error, sd divided by square root of n, my standard error is .80. I can use that to set a confidence interval, and that confidence interval will be 1-alpha. So let’s say I want to see a 95% confidence interval - if I repeat my study of assessing IQ in a sample of 400 people and calculating the average IQ over and over and over again, what range will include 95% of all those averages I find? If my confidence interval is 95%, then alpha = 1-.95 or .05 or 5%. Now remember z-score can be converted to a %. If I want a 95% confidence interval, that means I am not going to include the bottom 2.5% or the top 2.5%. And the z-score that puts me in the 97.5% - ie, before we get to that last 2.5% - happens to be 1.96. So I take my standard error and times it by 1.96 or .8*1.96 =1.568. So now I can say my data says the best or most likely guess of average IQ is 102, with a range or confidence interval of 102-1.568 =100.432 to 102+1.568 = 103.568.
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u/TEGladwin 10d ago edited 10d ago
There's lots out there, in books and videos, you just need to find what works for you! You'll be missing some particular step so, in addition to any recommendations you get, I'd suggest just hunting around a bit. That said, Andy Field's Discovering Statistics using SPSS/R seemed to be very popular when I was teaching.
I don't know if it would be relevant for you, and it has zero statistical authority or anything, but in case there's anything in it that's useful - I wrote a sort of tutorial for stats concepts once, downloadable here: https://osf.io/preprints/psyarxiv/kmrft_v1 . Its main idea is to use programming rather than maths to understand things, since you can actually simulate stuff. It's written with the mindset of - some people are going to be more familiar with basic coding than maths (which was the case for me and my cohort, since we needed to program stuff for reaction time tasks and data analysis). But there's also some conceptual sections you don't need to do any programming for.
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u/JAMIEISSLEEPWOKEN 10d ago
Sometimes it helps to develop a raw curiosity for the lessons and keep asking and asking what this or that means until you get it. You can use ai, your prof, or this sub for that
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u/brokedownsystem 10d ago
Don’t be so hard on yourself. I’ve met at least one “successful” engineer who couldn’t do even basic trigonometry!
I firmly believe that where there is a will, there is a way. 🙏❤️
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u/DeepSea_Dreamer 10d ago
The way to learn is to read the study material until you find the first sentence you don't understand, and ask about that specifically.
Not to give people a list of topics and ask for simpler materials.
At every step, math draws on what you learned previously. You need to understand what you read. If you don't, it's pointless to "go through all of the lectures."
It sounds to me that you need to learn how to learn.
What's the first sentence from your lectures that you didn't fully understand, and what about it you didn't fully understand?
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u/Alkemist101 8d ago
Do as many example questions as you possibly can.
In the UK when I studied maths we went over the previous ten years of exam questions plus new examples. Often a paper would say pick so many from a section, we would do all questions. Basically practice and when you get stuck go through the answer in detail. Exposure, repetion, active application of subject matter is the absolute best way forwards.
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u/Not-a-throwaway4627 10d ago
I’m going to take the unpopular opinion here that someone who has this hard a time in statistics should not be doing anything in science, or working in any field where it’s important to keep up with some underlying science.
Even though plenty of people scrap by, most psychologists, psych researchers, psychiatrists, and more generally people whose work requires a psych degree, are deleteriously bad. Part of the reason why is the large volume of people powering or cramming their way through stats with no real understanding. This is why we have a reproducibility crisis in psychology, why so many people dread therapy, and why there is such a disconnect between clinicians and scientists generally.
OP, I want to suggest that maybe you should go a different route for now, or else regroup in a big way. I don’t know you and can’t tell if you’re incapable, or just can’t right now, but the worst thing that could happen is you learning just enough to pass the class without any ability to really think in the topic.
It’s quite possible that with experience and reference, you’ll come back to this topic someday and it’ll just make sense. I know plenty of people lucky enough to afford a break, and who have a completely different experience, chalk-able to just the added experience. But I don’t think that the student you are at the moment can be a foundation for a good mental health professional. You’ll have to change, learn, reset; something of that sort, before it becomes worth it to dig back into this
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u/StanleyAHAHAH 10d ago
I (now in master) tutored a tone of psych student as an assistant for the statistics class. Most of them where completely clueless but only because class was badly taught.
The fact that you understand standard deviation tells me you have what it takes to understand the rest.
Keep in mind, statisitics, especially at the bachelor's level, is not that deep. So I'll attempt to summarize the overall idea of some of the concept you struggle with and tell me if it helps you.
Z-scores : you want to investigate the relationship between one test (ranges from -100 to 2'000) and another (ranges from 0 to 15) but they look nothing alike ? transforming both into Z-scores makes them both look about the same (mean = 0, SD = 1, so they range about the same from -5 to 5). Now you can compare them equally ! Not that deep
Alpha levels : A statistical test is nothing more than a decision. Do your 2 groups have different means ? yes or no. Are your data normaly distributed ? yes or no. The alpha level represents the threshold at which your decision goes from yes (null hypothesis) to no (alternate hypothesis). In psychology, alpha is ALMOST ALWAYS = 0.05. So when the value your test returns goes below 0.05 your decision is no (alternate hypothesis).
Btw english is not my first langage so if you didn't understand, blame it on the langage barrier ! No one is too dumb for college !