15 - Frequencies and Distributions Flashcards
(22 cards)
Ceiling effect
Occurs where measure produces most values near the top end of a scale
Customer rating 1-5 with many on 5. Should have had more options…
Central Limit Theorem
concept used to estimate how accurate your average result is when you have data from only a small sample.
Example: Suppose you want to know the average age of people in a city, but you can only survey 100 people. The Central Limit Theorem helps you estimate how close your average age from this small group is to the true average age of the entire city’s population. It tells you how confident you can be in your estimate given the limited data you have.
Deciles
Points on a measured scale that mark off each 10% of the data set or population
Distribution
shape and spread of data sets/populations
Floor Effect
Occurs where measure produces most values near the top end of a scale
Customer rating 1-5 with many on 5. Should have had more options…
Frequency
How often…
Frequency Distribution
distribution showing how often…
Kurtosis
statistical measure that describes the overall shape of a distribution in terms of its peakedness and the width of its tails compared to a normal distribution.
Example: Imagine you are analyzing the distribution of test scores in a class. If the test scores are distributed in a way that has a high kurtosis, it means the scores are concentrated more in the center, with relatively fewer scores in the tails compared to a normal distribution. This distribution would appear more peaked in the middle. On the other hand, if the kurtosis is low, it indicates that the scores are more dispersed and have thicker tails compared to a normal distribution, making the distribution flatter and less peaked in the center. Kurtosis helps us understand the shape and characteristics of a dataset’s distribution in relation to the normal distribution.
Leptokurtic Distribution
non-normal distribution that is closely bunched in the centre and tall.
Negatively skewed distribution
description of distribution that has longer tail of lower values.
Platykurtic distribution
non-normal distribution that is widely spaced out and low in the centre.
Positively skewed distribution
Description of distribution that contains a longer tail of higher values.
Example: some people making a lot of money when measuring the average in a town. Pulling “up” the score.
Quartiles
Points on a scale that mark the 25, 50 and 75th percentile of a distribution.
Sampling distribution (of means)
theoretical distribution that would be obtained by taking the same statistic from many same size randomly selected samples.
Example: test several random groups of 20 students math skills and make up a theoretical distribution for the whole school.
Sampling error
difference between a sample statistic and the true population statistic, usually assumed to be random in origin.
Basically the difference between what you test and the truth. Say you test the height of 100 students and get 182cm, but if you tested everyone you would get 184. Sampling error would be +2cm.
Skew/Skewed distributions
non-normal distributions that have a lot more extreme scores on one side of the mode than on the other
Standard error
Standard deviation of a sampling distribution. - It is often used to provide a range within which the true population parameter is likely to fall.
Example: Suppose you want to estimate the average height of all adults in a city. You take a random sample of 100 adults, measure their heights, and calculate the sample mean height. The standard error of this sample mean height indicates how much the sample mean is likely to differ from the true average height of all adults in the city. A small standard error means that your sample mean is likely a good estimate of the population mean, while a large standard error suggests more uncertainty in your estimate.
Standard Score (z-score)
number of standard deviations a particular score is from its sample mean.
Z-score/value (standard score)
number of standard deviations a particular score is from its sample mean.
Normal distribution (Gaussian)
symmetrical about mid-point. Bell shaped!
IQ, height etc..
Percentile
point on a measured scale that marks off certain percentages of cases in an ordered data set.
“Top tenth percentile” = 10 best in a class of 100
