Statistical Reasoning, Experimental Design and Statistics

Unit 0.6-0.7

Descriptive Statistics

Statistics that summarizes or describes features of a data set

Measures of Central Tendency

A single summary number that represents the middle, center, or typical value of a data set

Mean

The average value of a data set. Add all the values together and divide by the total number of data points.

Median

The middle value in a data set. Arrange all the data points in order from the lowest to the highest, then find the value that falls exactly in the middle.

Mode

The value that occurs most often in a data set. Count how many times each value occurs in the data set and find the value with the highest frequency.

Range

The distance between the highest and lowest values in a data set. Subtract the highest value from the lowest value.

Standard Deviation

How spread out the data points are around the mean. A small standard deviation means scores are close to the mean, a large standard deviation means scores are more spread out.

Correlational Co-efficienct

The direction and strength of the relationship between two variables. If the number is closer to +1.00, it is a positive correlation. If it is closer to -1.00, it is a negative correlation.

Normal Distribution

A symmetrical, bell-shaped distribution in which most scores are clustered around the center. Will create a curve with a peak in the center.

Positive Skew

A distribution in which unusually high scores create a long tail towards the higher values and pull the mean upward

Negative Skew

A distribution in which unusually low scores create a long tail toward the lower values and pull the mean downward

Bimodal Distribution

A distribution with two distinct peaks

Percentile Rank

How are a person’s score compares with the scores of other people in a group. For example, if you’re in the 80th percentile, your score is as high as or higher than approximately 80% of the comparison group.

Effect Size

Describes how large a difference or effect is. A larger effect size means a greater difference between two groups, while a smaller effect size means a lower difference.

Statistical Significance

Shows how unlikely it is for the results to have occurred by chance alone. Researchers often use p < .05 as the standard for statistical signifigance. p < .05 means the result is statistically significant, while p ≥ .05 means it is not statistically signifiant.

Measures of Variations

How clustered data values are within a dataset

Inferential Statistics

A branch of statistics that uses data from sample groups to make predictions about a larger group

P-Value

Statistics number that measures the likelihood of results from random chance alone, assuming there is no real effect

A p-value equal to or less than ___ shows statistical significance meaning the results are not likely due to chance. 

.05

A researcher wants to study the eating habits of American teenagers. She selects 1,000 teenagers from different states, including students from urban, suburban, and rural schools. 

Which term is best described by this scenario?

Representative Sample

Which of the following sets of scores has the greatest standard deviation?

2, 7, 9, 22

A psychologist wants to study how college students cope with stress. She selects 150 students from a university and gives them a questionnaire.

Which term describes the 150 students who participated in the study? 

Sample

For a language test with normally distributed scores, the mean was 70 and the standard deviation was 10. Approximately what percentage of test takers scored 60 and above?

84

A positive skew will have more data points on...

The low side of the scale

A psychologist surveys 500 students from one highly selective private school and finds that most students experience high levels of academic pressure. The psychologist wonders whether the same results would be found among students attending public schools throughout the country and wants to revise their experiment. 

Which term best describes what the psychologist is considering?

Generalizability

In the following scores, match the mean

4, 5, 6, 7, 8, 8, 9

6.7

In the following scores, match the mode

4, 5, 6, 7, 8, 8, 9

8

In the following scores, match the median

4, 5, 6, 7, 8, 8, 9

7

In the following scores, match the range

4, 5, 6, 7, 8, 8, 9

5