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Psychology Series # 5

 

04-25-12 11:31 PM
septembern is Offline
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Welcome to the fifth Psychology thread in the series, today and tomorrow will consist of statistical jabber a few guidelines of the American Psychological Association and a few things in between, I believe that this thread will wrap up the “Psychological Methods” section that the past three or so threads have been about. Today will primarily be just statistics.

In Psychology, descriptive statistics is a necessity to understand the basics of representation and understanding of the results received from the Psychological studies. I will go in depth to a good extent as I myself have taken a statistics course. When you receive data, it will often be in the form of number of people that qualify for each condition. This number we call the frequency. Thus when we hear terms like frequency distribution, what it really means is the different frequencies (number of subjects) for each category. This is usually what experimenters make from the conclusions, but it still is not presentable. One way of presentation is through histograms, though they have a special rule regarding the axes. Within these types of representative histograms, you will about always see the frequency on the y-axes, so just stick with that. The categories for which the frequencies are for, go on the x-axis. This is fairly simple thus far. With that you draw bars for each category and when they are all side by side, then the values can be compared and conclusions upon the data can be more readily made.

In order to get a good single estimate on what the average person wants, the middle of the data must be established, however, there are three different methods that are used to measure the central tendency of the data. Each of them are valid depending on the relative situation. The first is mean, which is quite simply the “average” system that is most commonly taught in schools. The mean is all of the data values added up and then divided by the total number of values and voila, you have the mean. The median is simply the middle value. This is really easy with an odd number of data points as the median is the middle value, but if there is an even number, then the middle two values are averaged (the number in the middle of the two). The mode is the number that reoccurs most often. However, it may be the case that more than one number is repeated the most number of times (there are two values which repeat the same number of times, and repeats the most overall), in which case it is possible to have more than one mode. A specific term for having two modes is called “bimodal”.

The reason why the mean, while most well-known, is not the only one used, is because the mean is not resistant to extreme values. Here is an example to understand what I mean by this: Say that you and about 20 friends all buy the same watch costing $19.95, however, Mr. Rich-guy comes along and shows the watch that he bought for $2000. If the 21 values are averaged up, then the average amount spent by each person is $114.24. But the problem is that NO ONE is even close to that value. That is not the true center that we are looking for. Extreme values as this one are regarded as outliers (however, there does exist an easy mathematical equation for determining whether it is actually an outlier, in this case it most definitely is). These extreme values pull the mean into a no-man’s-land when influenced by an extreme data point. This is where the median comes in handy, the middle cost will still be $19.95, so the median is not as easily influenced. The ability to not be significantly influenced by a few extreme values is called resistance. The median has more resistance than the mean and thus in cases where there are extreme values then it is wiser to use the median instead.

How spread out the data is can be statistically accounted for through range, standard deviation, and variance, all three with statistical equations to determine them. The variance is, quite simply, the square of the standard deviation, however, the variances are able to add, meaning that were you striving to add two values together, the variances can add as well. Standard deviations cannot.

No matter what distribution the data comes from, they can all be compared by changing the data point to a z-score. What happens with a z-score is that the mean and standard deviation are used in conjunction with the data point to create a number. This number can be changed into a probability using a table or a calculator and compared. Since the mean and the standard deviation of each group are involved scores from tests with completely different grading scales are able to be compared. Just for reference sake, the z-score is calculated by the point value minus the mean all over the standard deviation. Mean is often written as Mu, μ, and the standard deviation is written as sigma, σ.

Within statistics, there is a bell shaped curve that is called the normal distribution, while the z-score with the normal table is used for a probability and is not hard to calculate in itself, say you don’t have the table with you… there is a quick way to evaluate roughly where you might be. The 68 – 95 – 99.7 rule is a good one to remember. Approximately 68% of values lie between one standard deviation from the mean (between 1.00 and -1.00 z-score). Approximately 95% of values lie between two standard deviations of the mean (between 2.00 and -2.00 z-scores). Finally, approximately 99.7% of Z-scores lie within 3 standard deviations of the mean (between 3.00 and -3.00 z-scores). This also makes clear that what the z-score essentially is, is the number of standard deviations that one is from the mean of a normal distribution.

Percentiles are able to be found using the normal table, as the z-score has a particular proportion of values in the normal distribution that lie below the z-score stated. A percentile is defined as the percentage of people at or below the current score, so the proportions on the normal table are essentially the same thing.

Correlation was described earlier, so I do not feel any need to go deeper into that, but it is good to know that the correlation between two variables can be mathematically written as an integer between -1 and 1. As you get farther to the poles, then the correlation is stronger. +1 is a perfect, extremely strong positive correlation and the -1 is a perfect, extremely strong negative correlation. Plus or minus .9 is usually when the data can be defined as actually being strong. This number is called the correlation coefficient.

I will wrap up today with the line of best fit. What this is, is essentially a line created between the x and y values that you input as data from research that best figures the association between the two variables and creates an equation for a line based upon it. The line then can be used for predictions on certain x or y values that were not specifically tested. However, going too far out and making predictions is called extrapolation and means that the number might not be necessarily an accurate prediction.

I hope you were at least mildly interested in this statistical portion of Psychology, only a small paragraph on it tomorrow and then back into actual Psychology.
Welcome to the fifth Psychology thread in the series, today and tomorrow will consist of statistical jabber a few guidelines of the American Psychological Association and a few things in between, I believe that this thread will wrap up the “Psychological Methods” section that the past three or so threads have been about. Today will primarily be just statistics.

In Psychology, descriptive statistics is a necessity to understand the basics of representation and understanding of the results received from the Psychological studies. I will go in depth to a good extent as I myself have taken a statistics course. When you receive data, it will often be in the form of number of people that qualify for each condition. This number we call the frequency. Thus when we hear terms like frequency distribution, what it really means is the different frequencies (number of subjects) for each category. This is usually what experimenters make from the conclusions, but it still is not presentable. One way of presentation is through histograms, though they have a special rule regarding the axes. Within these types of representative histograms, you will about always see the frequency on the y-axes, so just stick with that. The categories for which the frequencies are for, go on the x-axis. This is fairly simple thus far. With that you draw bars for each category and when they are all side by side, then the values can be compared and conclusions upon the data can be more readily made.

In order to get a good single estimate on what the average person wants, the middle of the data must be established, however, there are three different methods that are used to measure the central tendency of the data. Each of them are valid depending on the relative situation. The first is mean, which is quite simply the “average” system that is most commonly taught in schools. The mean is all of the data values added up and then divided by the total number of values and voila, you have the mean. The median is simply the middle value. This is really easy with an odd number of data points as the median is the middle value, but if there is an even number, then the middle two values are averaged (the number in the middle of the two). The mode is the number that reoccurs most often. However, it may be the case that more than one number is repeated the most number of times (there are two values which repeat the same number of times, and repeats the most overall), in which case it is possible to have more than one mode. A specific term for having two modes is called “bimodal”.

The reason why the mean, while most well-known, is not the only one used, is because the mean is not resistant to extreme values. Here is an example to understand what I mean by this: Say that you and about 20 friends all buy the same watch costing $19.95, however, Mr. Rich-guy comes along and shows the watch that he bought for $2000. If the 21 values are averaged up, then the average amount spent by each person is $114.24. But the problem is that NO ONE is even close to that value. That is not the true center that we are looking for. Extreme values as this one are regarded as outliers (however, there does exist an easy mathematical equation for determining whether it is actually an outlier, in this case it most definitely is). These extreme values pull the mean into a no-man’s-land when influenced by an extreme data point. This is where the median comes in handy, the middle cost will still be $19.95, so the median is not as easily influenced. The ability to not be significantly influenced by a few extreme values is called resistance. The median has more resistance than the mean and thus in cases where there are extreme values then it is wiser to use the median instead.

How spread out the data is can be statistically accounted for through range, standard deviation, and variance, all three with statistical equations to determine them. The variance is, quite simply, the square of the standard deviation, however, the variances are able to add, meaning that were you striving to add two values together, the variances can add as well. Standard deviations cannot.

No matter what distribution the data comes from, they can all be compared by changing the data point to a z-score. What happens with a z-score is that the mean and standard deviation are used in conjunction with the data point to create a number. This number can be changed into a probability using a table or a calculator and compared. Since the mean and the standard deviation of each group are involved scores from tests with completely different grading scales are able to be compared. Just for reference sake, the z-score is calculated by the point value minus the mean all over the standard deviation. Mean is often written as Mu, μ, and the standard deviation is written as sigma, σ.

Within statistics, there is a bell shaped curve that is called the normal distribution, while the z-score with the normal table is used for a probability and is not hard to calculate in itself, say you don’t have the table with you… there is a quick way to evaluate roughly where you might be. The 68 – 95 – 99.7 rule is a good one to remember. Approximately 68% of values lie between one standard deviation from the mean (between 1.00 and -1.00 z-score). Approximately 95% of values lie between two standard deviations of the mean (between 2.00 and -2.00 z-scores). Finally, approximately 99.7% of Z-scores lie within 3 standard deviations of the mean (between 3.00 and -3.00 z-scores). This also makes clear that what the z-score essentially is, is the number of standard deviations that one is from the mean of a normal distribution.

Percentiles are able to be found using the normal table, as the z-score has a particular proportion of values in the normal distribution that lie below the z-score stated. A percentile is defined as the percentage of people at or below the current score, so the proportions on the normal table are essentially the same thing.

Correlation was described earlier, so I do not feel any need to go deeper into that, but it is good to know that the correlation between two variables can be mathematically written as an integer between -1 and 1. As you get farther to the poles, then the correlation is stronger. +1 is a perfect, extremely strong positive correlation and the -1 is a perfect, extremely strong negative correlation. Plus or minus .9 is usually when the data can be defined as actually being strong. This number is called the correlation coefficient.

I will wrap up today with the line of best fit. What this is, is essentially a line created between the x and y values that you input as data from research that best figures the association between the two variables and creates an equation for a line based upon it. The line then can be used for predictions on certain x or y values that were not specifically tested. However, going too far out and making predictions is called extrapolation and means that the number might not be necessarily an accurate prediction.

I hope you were at least mildly interested in this statistical portion of Psychology, only a small paragraph on it tomorrow and then back into actual Psychology.
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05-21-12 02:29 AM
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I too do psychology I'm on my last few modules now in sixth form before university. I don't know where you live but this kind of sounds like an American syllabus. In Britain we also study statistics.

But yes psychologists need empirical evidence to whatever theory they have in their head whether it be a 'one-tailed hypothesis' meaning a prediction that a test will render results which he would find to go in one direction. For example boy are better than girls would be a 1 tailed hypothesis whereas, there is a difference between boys and girls would be a two tailed hypothesis.
Either way proof is need and empirical evidence can't always be used if the data is subjective. There is 4 types of data; Interval, nominal, ordinal and ratio. 
Depending on your type of hypothesis, type of data used and study design. For example independent design, matched pairs, correlation, etc..
A series of statistical tests are available to you ranging from the Mann Whitney-U- test, wilcoxon, Chi Squared, etc... This kind of stuff is very mathematical though and hard to understand if you weren't taught, it involves critical values, P


As for mean results you right even though its the most commonly used it's affected by extreme samples as you've said, which is why psychologists use standard deviation to assess what the true average is while seeing how far away from the true average extreme variables are (called anomalies).
Sometimes however the mean is not needed and so mode, range and even median can show a better outline of a particular study. Another problem however is publication bias, for example 10 tests might prove that gaming gives you superpowers but in fact 100 other tests have said otherwise but did not get published because they had to accept their 'null hypothesis' (when they fail a stat test like a chi squared, etc..) and so do not get published.
But yeah nice thread glad to see other people study psychology here too there textbooks more stuff i could say on the subject but this is all i really need to revise on lol so thanks :p do you take an actual psychology course as well then?



I too do psychology I'm on my last few modules now in sixth form before university. I don't know where you live but this kind of sounds like an American syllabus. In Britain we also study statistics.

But yes psychologists need empirical evidence to whatever theory they have in their head whether it be a 'one-tailed hypothesis' meaning a prediction that a test will render results which he would find to go in one direction. For example boy are better than girls would be a 1 tailed hypothesis whereas, there is a difference between boys and girls would be a two tailed hypothesis.
Either way proof is need and empirical evidence can't always be used if the data is subjective. There is 4 types of data; Interval, nominal, ordinal and ratio. 
Depending on your type of hypothesis, type of data used and study design. For example independent design, matched pairs, correlation, etc..
A series of statistical tests are available to you ranging from the Mann Whitney-U- test, wilcoxon, Chi Squared, etc... This kind of stuff is very mathematical though and hard to understand if you weren't taught, it involves critical values, P


As for mean results you right even though its the most commonly used it's affected by extreme samples as you've said, which is why psychologists use standard deviation to assess what the true average is while seeing how far away from the true average extreme variables are (called anomalies).
Sometimes however the mean is not needed and so mode, range and even median can show a better outline of a particular study. Another problem however is publication bias, for example 10 tests might prove that gaming gives you superpowers but in fact 100 other tests have said otherwise but did not get published because they had to accept their 'null hypothesis' (when they fail a stat test like a chi squared, etc..) and so do not get published.
But yeah nice thread glad to see other people study psychology here too there textbooks more stuff i could say on the subject but this is all i really need to revise on lol so thanks :p do you take an actual psychology course as well then?



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05-21-12 10:18 PM
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aDrunkenFox : I actually use textbooks to self-study it currently.

Yes, I do live in America. Here a fair amount of people take statistics, like me, but it remains the minority. When looking at a career, the only subclass of Psychology that I actually will take is neuropsychology / biopsychology, but the others are interesting to learn.

Yep, inference proceedures, intervals, and all the like we learn. I do admit I did not go into many other tests besides the basic t-tests one and two sample, z-test one / two sample, proportion, difference of proportions, and chi squared goodness of fit, homogeneity, and independence. Those I actually ran and was tested in statistics. ANOVA and a few other ones I never learned over here.

Good times...good times. This stats stuff is pretty interesting... I loved all the brain stuff though. Learning and Behavior was interesting as well.
aDrunkenFox : I actually use textbooks to self-study it currently.

Yes, I do live in America. Here a fair amount of people take statistics, like me, but it remains the minority. When looking at a career, the only subclass of Psychology that I actually will take is neuropsychology / biopsychology, but the others are interesting to learn.

Yep, inference proceedures, intervals, and all the like we learn. I do admit I did not go into many other tests besides the basic t-tests one and two sample, z-test one / two sample, proportion, difference of proportions, and chi squared goodness of fit, homogeneity, and independence. Those I actually ran and was tested in statistics. ANOVA and a few other ones I never learned over here.

Good times...good times. This stats stuff is pretty interesting... I loved all the brain stuff though. Learning and Behavior was interesting as well.
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 septembern: Nice it's good to study what you enjoy anyway it gives you motivation which you seem to have in the subject so kudos



Across the pond in Britain we study statistics, relationships, psychopathology's in year 13 or '6th form' and a quite a few other topics last year. I completely agree though, that psychology has to be one of the most enjoyable subjects while I enjoy statistics the most because i like how all the systems work and stuff I find psychopathology's VERY interesting. It's just so surprising that even if your born with one slight malfunction in one part of the brain you could suffer from some really peculiar psychopathology's.



Have you read 'the man who thought his wife was a hat', If your into psychology I would definitely give that book a go, really interesting stuff.
Anyway I hope you do well in your studies, hopefully you'll get the career you want out of it and good Luck :p 

 septembern: Nice it's good to study what you enjoy anyway it gives you motivation which you seem to have in the subject so kudos



Across the pond in Britain we study statistics, relationships, psychopathology's in year 13 or '6th form' and a quite a few other topics last year. I completely agree though, that psychology has to be one of the most enjoyable subjects while I enjoy statistics the most because i like how all the systems work and stuff I find psychopathology's VERY interesting. It's just so surprising that even if your born with one slight malfunction in one part of the brain you could suffer from some really peculiar psychopathology's.



Have you read 'the man who thought his wife was a hat', If your into psychology I would definitely give that book a go, really interesting stuff.
Anyway I hope you do well in your studies, hopefully you'll get the career you want out of it and good Luck :p 

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