Midterm Lec 6b Flashcards
What are statistics?
The study of methods for:
-Describing and interpreting quantitative information
-Includes techniques for organizing and summarizing data
-Includes techniques for making generalizations and inferences from data
-Mathematical tests done on data collected from either populations or samples
Population
- The total collection of people, things, or events of interest
-N
Sample
-A subset of the population
-Smaller sets of cases selected frim a larger pool
-n
-Parametric statistical tests
-Not to be confused with population parameter
-Interval or ratio data
-Assume the data are normally (or near normally) distributed
Non-parametric statistical tests
-Data are counted (nominal scales) or ranked (ordinal scale)
-These statistics do not require a normally distributed population
Distribution of Scores
-Once we have collected our data, we can plot each data point in order to see the “shape” or “pattern” of the scores across the population or sample
Normal Distributions
- Normal distributions will have the same overall shape
- The exact shape of a distribution curve is described by the mean and the sd
- If you move the mean along the horizontal axis without changing the standard deviation, you will change the shape of the curve
- The mean is located at the centre of the symmetric curve, and will be the same as the median
- If you move the mean along the horizontal axis without changing the sd, you will change the shape of the curve
- The larger the sd, the more spread out the curve (aka flattening the curve)
- Normal Distributions: The 68-95 Rule
(Normal distributions)
In order to be considered ‘normal’ they should be:
- Symmetrical
- Single peaked
- Bell-shaped
The 68-95 Rule
In a NORMAL distribution:
68% of the observations will fall between the mean and the sd (+ /-1)
-34.13% to the left, and 34.13% to the right of the mean
95% of the observations will fall between the mean and two sd’s (+ /-2)
-47.5% to the left, and 47.5% to the right of the mean
99.7% of the observations will fall between the mean and three sd’s (+ /-3)
-49.8% to the left, and 49.8% to the right of the mean
Normal Distributions
-Why don’t standard deviations add up to 100%?
-The 0.3% remaining is equal to 0.15% in each end or tail
-Represents extreme scores and as such, are relatively rare
Standard Deviation sd
measure of the amount of variation such as spread, desperation from the mean exits
Two key characteristics of a distribution of scores
Central tendency: The value of a “typical” score
Variability: The extent to which scores differ from one another
Measures of Central Tendency
Mean / Median / Mode
Mean
-The most common measure of central tendency
-Quickest estimate of central value and shows the most typical case
-Sensitive to extreme scores
-Add all the scores and divide by the number of scores
-Not a great representation of all the scores
Median
-A measure of position; score that lies in the middle
-Not sensitive to extremes and therefore may be a more realistic measure of CT than the mean
How to calculate Median
Step 1:Organize the data in the list from lowest to highest
- This
- 2 5 8 10 5 7 4 6 6 9 1 3 5
- Becomes
- 1 2 3 4 5 5 5 6 6 7 8 9 10
Step 2: Determine if there is an even or odd number of data points (e.g., scores)
E.g., does the list contain an odd number of data points? 13, 21, 53 numbers
E.g., does your list contain an even number of data points? 6, 14, 22
Step 3a: For lists with an ODD set of numbers
- Choose the number in the middle of the list wherein ½ of the numbers are above, and ½ of the numbers are below
- 1 2 3 4 5 5 5 6 6 7 8 9 10
- There are 6 numbers above, 6 numbers below
Step 3b:For lists with an even set of numbers
Calculate the half way point between the two middle scores
- For this example, use the same list from before, remove the first 5 (you should now have 12 numbers)
- 1 2 3 4 5 5 6 6 7 8 9 10
- Choose the second 5 and the first 6
- Median = 5 + 6 = 11 / 2 = 5.5
- Median = 5.5
Mode
-The most frequently occurring / obtained score
1 2 3 4 5 5 5 6 6 7 8 9 10
Mode = 5
Variability
The extent which scores differ from one another
Three measures of variability
Range
Variance
Standard Deviation
Range
-Simplest measure of variation
-Difference between the highest and lowest scores
-Not generally used because it only takes into account the extreme scores, not the majority of scores
Step 1:
- Organize your scores in from lowest to highest
- 1 2 3 4 5 5 5 6 6 7 8 9 10
Step 2:
- Range = highest score - lowest score
- E.g., range = 10 - 1 = 9
