Module 15: Inferential statistics Flashcards
What is the difference between descriptive statistics and inferential statistics?
Descriptive statistics is summarizing or describing data from popylations and inferential stats is maing inferences from distributions (analyze samplings to make predictions about larger populations)
The normal distribution
Desccribes a very common probability distribution of values of a continous variable around the mean, no skew
Graph of a normal distribution is called
The normal curve
Vertical axis of the normal curve
Frequency of values
Horizontal axis of the normal curve
Scale of continous values, what we are measuring
Properties of a normal distribution (4)
- symmetrical
- unimodal
- bell shaped curve
- mean mode and median are equal
Spread of normal distribution is determined by—– larger spread means —–
standard deviation
larger SD
About —% of the data lie within 1 SD of the mean
68%
About —% of the data lie within 2 SD of the mean
95%
About —% of the data lie within 3 SD of the mean
99.7%
The standard normal distribution
A normal distribution with a mean of 0 and a standard deviation of 1
Properties of the standard normal deviation (2)
- The cumulative area is close to 0 for Z scores close to z=+/- 3.49
- The cumulaytive area increases as the Z score increases
Z-table
Table with pre-calculated areas under the curve up to each value for Z for a standard normal distribution
Standardization+formula (2)
Turning data into a standard normal distribution
- use the formula z=(x-mean)/SD
If you are trying to find the Z score for anything below the mean, your 2 scores should be
negative
a Z score of -3.45 means
more than 3 SD below the mean
Z score tells us
how many units you go above and below the SD
Larger proportion is —- side for + Z score and —- for - Z score
- left
- right
Percentile always mean
everything from the far most left side until that said percetile.
Areas are never
> 1
sampling error
Random variability between observations or statistics that is simply due to chance
Sampling Distribution + formed when (2)
- The distribution of a statistic over repeated sampling from a specified population
- Formed when samples of sample size n are repeatedly taken from a population
The central limit theorem
The larger the sample size that we draw from a population the more normal the sampling distribution of the sample mean becomes, regardless of the shape of population
If we take samples of this distribution, cailate their means and then graph them as long as those sampels are big enough >=30, then when we graph that sample distribution it would be —- and centered around —-
- normally distributed
- population mean
Greater the sample size, the more precise/less variability in the
sample means
You can only use Zed tables when
it is normally distributed
If the population itself is normally distributed, the sampling distribution of the sample means is —– for any —-
- normally distributed
- sample size n
In both case where you have sample >=30 or a normal distribution, according to the CLT, the sampling distribution of sample means has (3):
- A mean equal to the population mean
- A variance equal to 1/n times the variance of the population
- A standard deviation equal to the population SD divided by the square root of n
SD and variane of pop and sample formulas:
Zed score formula for transforming single scores and sample mean into a zed score:
