1. Introductory Statistics
How to interpret the statistics you encounter in research

2. What is statistics?
A numerical description of data that describes the sample and helps make inferences about a population
Population-consists of all the individuals who make up a group that one is interested in studying
Ex: 9th graders in New York City public schools
Sample- consists of a large group of individuals randomly drawn from the population to reflect the populations’ characteristics
Ex: 800 9th grade students from 4 NYC public high schools

3. Sample or Population
Determine which of the groups below would be considered a population or a sample
All the Females in North America
All the high school math text books
All females surveyed outside of a chain supermarket in 25 states
All the boys in PS 29
All the boys in Elementary school
Each fifth title from an alphabetized list of titles of high school math text books

4. Why use statistics?
To summarize data and reveal what is typical and atypical
To show the relative standing of an individual among the group
To estimate error that may have occurred in sample selection
To test for statistical significance of findings

5. What is statistical significance?
Significance permits one to conclude that a particular finding is probably real for the population rather than a result of sampling error.
Consider the following statement:
Ex: 78% of boys in PS 29 did not intake a sufficient amount of daily calcium
(If 78% is large enough, then the findings can be generalized to the population of all elementary school boys)

6. Probability and Statistics
Since one studies and/or measures samples of populations, one hopes to show that the findings made for the sample will apply for the population
Probability levels are assigned that allow one to say that the sample finding is probable for the population

7. Probability
For example if you read that p<.05, that means that there is less than a 5% percent chance that the results you obtained were due to sampling error.
Therefore a researcher that claims that p<.05 would be considered having a 95% confidence interval.
Most scientists would like to have a 99% confidence interval which suggests that p<.01 which means that there is less than 1% chance that the results were obtained due to chance or sampling error.

8. Why use statistics?
To summarize data and reveal what is typical and atypical
To show the relative standing of an individual among the group
To estimate error that may have occurred in sample selection
To test for statistical significance of findings

9. What does the following mean?
Typical- Normal
Atypical- Abnormal

10. How to summarize data and reveal what is typical and atypical
Measures of Central Tendency
Mean (arithmetic average)
Ex: 9,8,8,7,7,7,4,4,3,3 X̄=
Median (midpoint in scores)
Ex: 9,8,8,7,7,7,4,4,3,3 Mdn =
Mode (most frequent occurring score)
Ex: 9,8,8,7,7,7,4,4,3,3 Mo =
Lets practice!!!

11. Why use statistics?
To summarize data and reveal what is typical and atypical
To show the relative standing of an individual among the group
To estimate error that may have occurred in sample selection
To test for statistical significance of findings

12. How to show the relative standing of an individual among the group
Measures of Variability
Range (shows the distance from the highest to the lowest score)
Ex: set A 9,10,10,10,10,10,10,10,10,11
set B 1,3,5,7,9,11,13,15,17,19
Set A R=11-9
Set B R=19-1
Interesting, because the mean and mode for both sets are? ________

13. How to use Range? How is sample A different from sample B?
set A 9,10,10,10,10,10,10,10,10,11
set B 1,3,5,7,9,11,13,15,17,19
If a researcher is working with an independent variable that treats a specific condition, the researcher may require a sample with similar participants.
One uses range when you are looking for a sample that does or does not deviate much from the mean.
In the above example Sample A has less of a range then sample B.
Lets practice!!

14. How to show the relative standing of an individual among the group
Reminder: Range tells us the difference between the largest and smallest values, it does not tell us how much other values vary from one another or the mean.
Deviation
Variance
(Both show how individual scores vary from the mean)
To determine deviation :
Consider the following set of data:
9,8,8,7,7,7,4,4,3,3
Raw score – Mean = Deviation Score (how much each score differs from the mean)
Ex: = 3 (therefore the score of 9 is three points away from the mean)

15. How to use a deviation score?
Ex: = 3 (therefore the score of 9 is three points away from the mean)
Therefore a researcher may find that a participant weighs three pounds more than the average weight of participants in the sample selected.
Deviation may be determined for each score but variance is determined in order to calculate Standard Deviation.
Lets use a chart to help us determine variance….before moving to Standard Deviation.

16. Calculation of Deviation and Variance
Raw Score
Raw score – mean= Deviation
(Raw score - mean)² 9 3 8 2 4 7 1 -2 -3
Sum =60
Sum =0
Sum =46
Mean =6
Above number shows how each score deviates from the mean
Variance= (sum of all squares)÷ (number of scores - 1)
( 46÷ 9=5.11)

17. Standard Deviation
Standard deviation is the square root of variance therefore…….
SD=
Standard deviation is the most accurate statistical analysis you should be using to determine if your data results do not deviate from what is normal.
Lets practice!!!