Midterm Lec 6b

Question 1

What are statistics?

Answer 1

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

Question 1

Population

Answer 1

• The total collection of people, things, or events of interest
  -N

Question 2

Sample

Answer 2

-A subset of the population
-Smaller sets of cases selected frim a larger pool
-n

Question 3

-Parametric statistical tests

Answer 3

-Not to be confused with population parameter
-Interval or ratio data
-Assume the data are normally (or near normally) distributed

Question 4

Non-parametric statistical tests

Answer 4

-Data are counted (nominal scales) or ranked (ordinal scale)
-These statistics do not require a normally distributed population

Question 5

Distribution of Scores

Answer 5

-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

Question 6

Normal Distributions

Answer 6

• 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

Question 7

(Normal distributions)
In order to be considered ‘normal’ they should be:

Answer 7

• Symmetrical
• Single peaked
• Bell-shaped
  The 68-95 Rule

Question 8

In a NORMAL distribution:

Answer 8

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

Question 9

Normal Distributions
-Why don’t standard deviations add up to 100%?

Answer 9

-The 0.3% remaining is equal to 0.15% in each end or tail
-Represents extreme scores and as such, are relatively rare

Question 10

Standard Deviation sd

Answer 10

measure of the amount of variation such as spread, desperation from the mean exits

Question 11

Two key characteristics of a distribution of scores

Answer 11

Central tendency: The value of a “typical” score
Variability: The extent to which scores differ from one another

Question 12

Measures of Central Tendency

Answer 12

Mean / Median / Mode

Question 13

Mean

Answer 13

-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

Question 14

Median

Answer 14

-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

Question 15

How to calculate Median

Answer 15

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

Question 16

Mode

Answer 16

-The most frequently occurring / obtained score
1 2 3 4 5 5 5 6 6 7 8 9 10
Mode = 5

Question 17

Variability

Answer 17

The extent which scores differ from one another

Question 18

Three measures of variability

Answer 18

Range
Variance
Standard Deviation

Question 19

Range

Answer 19

-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