STATISTICS STATISTICS Numerical data

How Do We Make Sense of the Data? descriptively Researchers use statistics for two major purposes: (1) descriptively to characterize measurements made on groups or individuals inferentially (2) inferentially to judge whether these measurements are the result of chance

How can data be so nonsensical?! Statistics are confusing. They can be counterintuitive. Take the Monty Hall problem, for instance. GlGghttp:// GlGg

Statistics are used to makes sense of the data Frequency Distribution:Frequency Distribution: A chart showing how frequently each of the various scores in a set of data occurs Frequency Distribution organizes the raw data, making it more easily interpreted

Histogram A graphical display of tabulated frequencies, shown as bars

Descriptive Statistics Numbers that describe the main characteristics of the data Statistical procedures used to describe characteristics and responses of groups of subjects Basic Purpose: To observe and record behavior

Describing the Data With Descriptive Statistics Descriptive statistics include: The mean The median The mode The range The standard deviation The normal distribution

Measures of Central Tendency Central Tendencies are Averages The central point around which the scores seem to cluster Mean, Median, Mode, Range All are descriptive statistics and measures of central tendency All are descriptive statistics and measures of central tendency

An “average” family dilemma Suppose your mother has planned a family reunion on Sunday when you and other family members have other things to do. Your family really protests saying that they don't want to spend the day with a bunch of "old fogies." Your mother attempts to convince each family member separately that the reunion won't be so bad.

Mom always knows best… Mom says to your younger sister that the average age is 10, tells you that the average age is 18, and tells your dad that the average age is 36. Now each family member feels better about spending the day at the family gathering.

And how to use statistics to her advantage… The following chart has the ages of those attending the reunion: Age Name/relation cousin Susie cousin Joey twin Shanda twin Wanda cousin Marty cousin Juan cousin Pat Aunt Harriet Uncle Stewart Aunt Rose Uncle Don Grandma Faye Great Aunt Lucy Belle

And your demise… Was your mom telling the truth? Why or why not? Average age is 10= Average age is 18= Average age is 36= The perception (and the distribution) is definitely skewed.

: the of a distribution The Mean: the average of a distribution (as in a mean GPA) (as in a mean GPA) : in a distribution The Median: the middle score in a distribution (Think Med as Mid…as in middle) (Think Med as Mid…as in middle) the score in a distribution The Mode: the most often occurring score in a distribution (Mode sounds like ‘Most’) (Mode sounds like ‘Most’)

The Range: The difference between the lowest and highest scores in a distribution

Median Best measures of central tendency to examine data 1. Less resistant to extreme scores than the mean 2. More reflective of the data than the mode Ex: pay scales, salary, house costs

The Mean The measure of central tendency that is most affected by extreme scores

The Standard Deviation The Standard Deviation The average difference between the scores and their meanThe average difference between the scores and their mean Takes into account all of the scoresTakes into account all of the scores

The Normal Distribution A bell shaped curve describing the spread of a characteristic throughout a population

The Normal Distribution 68.26

Correlation A relationship between two variables, in which changes in one variable are reflected in changes in the other variableEXAMPLE A child’s height  age Education  income

Correlation Coefficient A number between -1 and +1 expressing the degree of relationship between two variables Does NOT tell about cause and effect Simply gives information on the direction and strength of the relationship

Positive Correlation If people have high scores on one variable also have high scores on another, the correlation is positive. The correlation coefficient is also positive. (ex: +.09)

If there is a positive correlation between the number of children a person has and overall life satisfaction, we would find that people with more children… ….are more satisfied with their lives than are people with fewer children.

Negative Correlation Negative Correlation If people have high scores on one variable, but low on another, the correlation is negative The correlation coefficient is also negative…(less than 0) The correlation coefficient is also negative…(less than 0)

If a study finds that there is a negative correlation between exercise and blood pressure, this would most likely indicate that…. …people who exercise more tend to have lower blood pressure.

Zero Correlation Zero means there is no relationship between scores

If you measured the height of each student in class and the amount of money that each person has in his or her pockets, you would expect to find…. …a zero correlation.

Making Inferences with Inferential Statistics Inferential statistics are used to assess whether the results of a study are reliable or whether they might be simply the result of chance Often used to determine (or ‘infer’) whether two or more groups are essentially the same or different

Sampling Random Sample A sample group of subjects selected by chance Representative Sample A carefully selected sample of a targeted group, such as customers, whose characteristics represent (as accurately as possible) the larger population Example: A Gallup Poll….only a few hundred participants provide an accurate assessment

Statistical Significance Results of an experiment must reach the level of statistical significance to ensure the results are not due to chance. Psychologists accept a difference between groups to be ‘real’ or significant when the probability that it might be due to chance is less than 5 in 100.

Statistical Significance When a statistic is significant, it simply means that you are very sure that the statistic is reliable. It doesn't mean the finding is important. p<.05 = chance of very little influence p<.01 = (less 1 in 100) more strict p<.001 = (less 1 in 1000) more strict Significance levels of at least.05 are sought;.01 is better.

Question: If a study resulted in a large p value (such as p>.50), what could we say about the results? Answer: There is a high probability that we received these results just by chance.

End of Chapter 2