normal distrabiton Flashcards
Mean
The sum of all values divided by the number of
values
Median
The middle value when all values are arranged in
ascending or descending order. If thereβs an even number of
observations, it is the average of the two middle numbers
Mode
The value that appears most frequently in the data set
Range
The difference between the highest and lowest values in
the data set.
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Variance
The average of the squared differences from the
Mean. It measures how spread out the values are.
Standard Deviation:
how much data is incorparated
he square root of the variance,
representing the dispersion of the dataset relative to its mean
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law of large numbers
problem with latrge numbers
30+ sample sizes = we can use the stats
A one in a million occurrence happens 10x a
week in Calgary..
z score formula
what do you need for it
Z = ππππ βΞΌ/
Ο
* X i = individual score & ΞΌ is the population mean
* Ο = population standard deviation
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Definition of a z-score
Are expressed in terms of standard deviations from their means.
* Are a measure of how many standard deviations a raw score is
below or above the population mean.
* Have a distribution with a mean of 0 and a standard deviation of 1.
assumptions of a z score
Need interval or ratio data (continuous variables)
* Need to know the population mean & variance
normally distributed population
when might a z score not work
small sample size
prurpose of z score
Standardize a group of scores
* Compare scores from a measure/test to a
normal distribution.
* Standardize a group of variables for
compariso
What does a statistical tool like the Z-Score tell us?
Z- scores underline the importance of considering
variance or the standard deviation when understanding
a score.
* Because everything is normalized to 1 standard
deviation, with a z-score we can literally compare apples
and oranges if we want
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whats the diffrence btween z and t scores
t scores are for groups
a reselts has statistical signifcants when we
see diffence in the mean
alpha levels establish a
likelihood of seeing a difference, when
considering the error for a given measurement instrument
* Recorded score = true score + error
* Error = confounding variability in the measure
Alpha (Ξ±)
s the significance level you choose for a hypothesis test.
It represents the probability of rejecting the null hypothesis when it is true (Type I error).
the p-value
s the probability of obtaining test results at least as extreme as the observed results, under the assumption that the null hypothesis is correct.
Your chosen alpha (Ξ±) determines the threshold for significance. If the p-value is less than Ξ±, you reject the null hypothesis.
o with a line on top of it
population standerd diviation
u
population mean
s
sample standerd duvation
x with line on top
sample mean
