Populations, Parameter and Interferance Flashcards
Can populations be pictured by histograms
No populations are not samples and therefore can’t be pictured as they are often conceptual.
Why do we have a sample of a population
From a sample of a population you can make INFERENCES about the population
How to prevent a sample bias
Randomly select a sample
How to ensure validation and correct inferences
Need to decide how large the sample size is
What does a normal distribution look like
The curve has a central peak with the curve descending SYMMETRICALLY o either side
What does the height of the curve indicated in a normal distribution
The height of the curve indicates the most values of the population fall near the central value with fewer values further from the centre
What does the symmetrical decline in a normal distribution tell us?
Tells us that their are equal amounts of the population located at the same distance above the peak as there is at that distance below the peak
What is different within normal distribution?
The location of the data- determined by the position of the central peak
The spread of data
The dispersion of data -width of the bell
How is the location and the dispersions of data in a normal distribution determined by
They are determined by two POPULATION PARAMETERS:
- Peak is located at the population MEAN
- The width is determined by the population standard deviation
What are the population parameters in the normal distribution
- Mean
- Standard Deviation
How to calculate population parameters?
Population parameters are unknown. There are sample analogs of population parameters and they can be estimated from sample data known as SAMPLE STATISTICS.
How to calculate the sample mean of a distribution?
Adding all numbers up and dividing by number of values
What parameters can be used of the data is not normally distributed
- Median
- Quartiles
Why use a a median instead of mean for non normal distribution
The mean is sensitive to the values of a few LARGE OBSERVATIONS in a way median is not
Why can’t you be too eager to jump to median and qualities>
-Inefficient analysis
- Unnatural analyses
Name a method that can be used to deal with non-normal data
Transforming data
The whole area underneath the bell-shaped curve equals what?
1
What is the value of probability corresponding to a given X
It is the cumulative probability of the distribution at X or the Cumulative distribution function at X
What is the probability that a value is above X
1-X
What does Q normally represent in a normal distribution curve
The probability of being above an equal number of units above the mean (probability height)
Does each X in a normal distribution curve have a corresponding P
Yes, P depends only on that multiple of alpha above or below the mean (Z), not on the values of u and alpha
What is the advantage of knowing that P (Probability) depends ONLY ON THE Z-VALUE
It gives considerable aid to understand your data and its distribution
Where does 95% of the values in a normal distribution lie
95% lie within two standard deviation of the mean
What does the interquartile range equal for a normal distribution
1.36alpha
What does the smaller sample size do to the normal distribution curve
There are less extremes than a larger sample size
What does the range for a normal distribution represent
The spread of measurements and sample size
Why is the normal distribution important in statistics?
- Arises empirically- many statistical techniques for analysing normal distributed data are ROBUST and not affected by modest departures from normality
- Some VARIABLES are normally distributed because the BIOLOGICAL MECHANISM CONTROLING THEM such as variable polygenic control
- DEPARTURE FROM NORMALITY DECREASES AS THE SAMPLE SIZE INCREASES- If the population is very skew the effect is noticeable even in samples as small as 10
