1. Why include statistics as part of Psychology?
Doing psychology research
Reading psychology research articles
Analytical reasoning, critical thinking
Statistics
Fundamental tool for all scientific inquiry
Way of making sense out of data

2. Populations and Samples
the group of individuals (or things) of interest in a particular study
For example, a researcher may be interested in the relation between class size (variable 1) and academic performance (variable 2) for the population of third-grade children.
Sample
Usually populations are so large that a researcher cannot examine the entire group
a sample is selected to represent the population in a research study
Sample size depends on the type of research
The goal is to use the results obtained from the sample to help answer questions about the population

3. Sampling from a Population

4. Figure 1-1 (p. 6) The relationship between a population and a sample.
Make an Inference
representative of the population

5. Variables And Data
A variable is a characteristic or condition that can change or take on different values
Most research begins with a general question about the relationship between two variables for a specific group of individuals. (similar to forming an hypothesis)
Data are measurements or observations
The measurements obtained in a research study are called the data or data set
Each measurement is a datum (singular) or score
The goal of statistics is to help researchers organize and interpret the data. 5

6. Sources of Data Observation Research Survey Research Experiments
Naturalistic no intervention
Poor control
Correlational data
Survey Research
A correlational method of collecting data
Do not exercise any control over time order
Poor control of alternatives
Can show relationships
Experiments
Exercise control over covariation, time order and alternatives
Can help establish causation

7. Using Statistics in Psychology
Carrying out psychological research using an empirical approach means the collection of data. Statistics are a way of making use of this data
Descriptive Statistics: used to describe characteristics of our sample
Inferential Statistics: used to generalise from our sample to our population
Any samples used should therefore be representative of the target population

8. Descriptive Statistics
Descriptive statistics are methods for organizing and summarizing data.
For example, tables or graphs are used to organize data, and descriptive values such as the average score are used to summarize data.
A descriptive value for a population is called a parameter and a descriptive value for a sample is called a statistic. 8

9. Inferential Statistics
methods for using sample data to make general conclusions (inferences) about populations
a sample is only a part of the population
sample data provide only limited information about the population
sample statistics are imperfect representatives of the population parameters because of sampling error 9

10. Sampling Error
The discrepancy between a sample statistic and its population parameter is called sampling error.
Defining and measuring sampling error is a large part of inferential statistics. 10

11. Sampling from a Population

12. Figure 1-2 (p. 9) A demonstration of sampling error
Figure 1-2 (p. 9) A demonstration of sampling error. Two samples are selected from the same population. Notice that the sample statistics are different from one sample to another, and all of the sample statistics are different from the corresponding population parameters. The natural differences that exist, by chance, between a sample statistic and a population parameter are called sampling error.

13. Is an example of sampling error
Margin of Error Box 1.1
Is an example of sampling error
Terminology used in polling data such as political polls
Amount of error between a sample statistic and a population parameter
There will always be sampling error in:
survey research
experiments

14. Figure 1-3 (p. 10) The role of statistics in experimental research.

15. Relationship Between Variables
Correlational Method
Measuring two variables for each individual
Height and Weight
SAT and GPA
Wake-up Time and Academic Performance (Figure 1.4)
Determine the relationship between the variables
Limitations of the correlational method
Can not demonstrate cause-and-effect relationships

16. Figure 1.4
One of two data structures for studies evaluating the relationship between variables. Note that there are two separate measurements for each individual (wake-up time and academic performance). The same scores are shown in a table (a) and in a graph (b).
Figure 1.4
One of two data structures for studies evaluating the relationship between variables. Note that there are two separate measurements for each individual (wake-up time and academic performance). The same scores are shown in a table (a) and in a graph (b). 16

17. Hypothetical data showing results from a correlational study evaluating the relationship between exposure to TV violence and aggressive behavior for a sample of 10 children. Note that we have measured two different variables, obtaining two different scores, for each child. The data show a tendency for higher levels of TV violence to be associated with higher levels of aggressive behavior.

18. Relationship Between Variables
Comparing two groups of scores
Experimental (see Figure 1.5 )
One variable defines the groups (violence vs no violence)
Independent variable
Another variable is the measurement, scores from the groups
Dependent variable
NonExperimental “quasi-experimental”
Natural or pre-existing groups such as gender which are selected not manipulated
Before and after measurements for example before and after therapy
Do not confuse with control vs experimental groups
There is only one group of participants whom get measured twice

19. Figure 1. 6 The Structure of an experiment
Figure 1.6 The Structure of an experiment. Participants are randomly assigned to one of two treatment conditions: counting money or counting blank pieces of paper. Later, each participant is tested by placing one hand in a bowl of hot (122 F) water and rating the level of pain. A difference between the ratings for the two groups is attributed to the treatment (paper vs money). 19

20. The structure of an experiment
The structure of an experiment. Volunteers are randomly assigned to one of two treatment conditions: a 70° room or a 90° room. A list of words is presented and the participants are tested by writing down as many words as they can remember from the list. A difference between groups is attributed to the treatment (the temperature of the room).

21. In this experiment, the effect of instructional method (the independent variable) on test performance (the dependent variable) is examined. However, any difference between groups is performance cannot be attributed to the method of instruction. In this experiment, there is a confounding variable. The instructor teaching the course varies with the independent variable,so that the treatment of the groups differs in more ways than one (instructional method and instructor vary).

22. Figure 1-7 (p. 17) Two examples of nonexperimental studies that involve comparing two groups of scores. In (a) the study uses two preexisting groups (boys/girls) and measures a dependent variable (verbal scores) in each group. In (b), time is the variable used to define the two groups, and the dependent variable (depression) is measured at each of the two times.

23. NonExperimental “quasi-experimental” Terminology
Similar data structure to experiments
One variable identifies groups (independent)
A second variable is measured to obtain data (dependent)
For nonexperimental
Independent variable such as gender is not manipulated
So it is called “quasi-independent variable”

24. Data Structures and Statistical Method
Data structure is used to classify statistical methods
One group with two variables measured for each individual
Survey research
Collect GPA and SAT scores for each person
Use correlational statistics to describe the data
Survey or Observational Research
Number of individuals in a group
Groups based on “natural” categories such as gender
Groups based on some activity such as “talk” vs “text” (table 1.1)
Use Chi-square statistic to describe the data
See scales of measurement on page 23

25. Data Structures and Statistical Method
Data structure is used to classify statistical methods
Two or more groups of scores
Compare two groups such as “Money” and “Paper” (fig 1.6)
Two groups of individuals
Compare average from each group of scores
Several different statistical tests are used such as t-test or ANOVA based on number of groups

26. Constructs and Operational Definitions
To form a hypothesis from a research question the researcher needs to define the variables
What the effects of drug “Bulk-O” on weight gain?
Independent variable is drug or no drug
Dependent variable is weight gain which is “concrete”
What are the effects of drug PQX1450 on Anxiety?
Dependent variable is “anxiety” which is a construct
so we need to define the construct of anxiety
Need an Operational Definition for anxiety
How intelligent are students taking Methods course?

27. Variables And Measurement
Discrete Variable
Discrete categories such as students, cars, houses
Usually a count of the number of individuals or things
number of students in class
number of cars in the parking lot
number of houses along the street
Also called “Categorical variables”
Sometimes referred to as “Qualitative variables” which is confusing because qualitative is just description not counting
Continuous Variable
Variable can be divided into an infinite number of values
height, weight, time

28. Use of Real Limits with Continuous Variables
When working with continuous variable
Can adjust precision by changing units
Hours vs Minutes vs Seconds up to the limit of accuracy for the measuring device such as a wall clock or a stop watch
Because a variable such as weight is infinitely divisible the researcher needs to set boundaries or limits
use real limits which are boundaries located exactly half-way between adjacent categories.
Researcher decides where to set limits as a practical matter such as record weight to the nearest pound
So if someone has weight of they are in 150 data
Each value “150” is an interval with upper and lower limits
Values that fall on the boundary “150.5” can be rounded up or down just be consistent with the rounding rule 28

29. Figure 1.8 p.21 When measuring weight to the nearest whole pound, and are assigned the value of 150 (top). Any value in the interval between and is given the value of 150.

30. To establish relationships between variables, researchers must observe the variables and record their observations. This requires that the variables be measured. The process of measuring a variable requires a set of categories called a scale of measurement and a process that classifies each individual into one category.
Measuring Variables 30

31. Four Types of Measurement Scales :
Nominal (by name / category)
Ordinal (by order / rank)
Interval (meaningful, equal interval scaling)
Ratio (interval with a “real”zero point –degrees Kelvin)

32. Nominal Scale “Names” Classifying subjects into categories
Scales of Measurement
Nominal Scale
“Names”
Classifying subjects into categories
No category is “more” or “less,” just different
Categories can be labeled by
words (e.g., Male, Female) or
numbers (e.g., 0, 1) which can be confusing
Nominal scale always yields discrete variable

33. Ordinal Scale “ordered” Categories are in ordered sequence, ranked
Scales of Measurement
Ordinal Scale
“ordered”
Categories are in ordered sequence, ranked
Examples:
Gold, silver, bronze medals
Don’t know how far gold was from silver, or silver from bronze
Class standing (33rd out of 108)
Ordinal scale technically yields discrete variables (can not be ranked 33rd and a half)
Different statistical procedures are required.

34. Scales of Measurement
Interval Scales
Distance between two values is the same at any point on the scale
The difference between scores of 6 and 10 is 4 units
The difference between scores of 26 and 30 is 4 units
Interval scale does not have absolute zero
Attitudinal scales, on a scale of from 1(not a all) to 10 (a great deal) how much do you like anchovy pizza?
Example 1.2 page 25: convert ratio scale to interval scale
Height measurements (ratio scale) can be converted to difference scores i.e. difference from the average score
Average height of 50 inches so a height of 52 becomes a difference score of +2 which is an interval scale measurement

35. Ratio Scales But what about
Scales of Measurement
Ratio Scales
In addition to having even intervals we can calculate ratios so a
Ratio scale has meaningful, absolute zero
Distance: zero distance
Weight: zero weight
Temperature: absolute zero but not zero degrees Fahrenheit
Time: zero time ??
But what about
IQ score? Interval
Score on test of neuroticism? Interval

36. Scales of Measurement
In practice, many psychological variables give more than ordinal-level information, but not possible to clearly establish that they are interval-level. Generally treated as interval data.
Many statistical procedures assume at least interval level data, but function reasonably well with ordinal-level data

37. Statistical Notation
X is a discrete variable, where 0=men and 1=women.
Y is a continuous variable, representing years of age.
Subject#
Gender (X)
Age (Y) 1 8 2 10 3 7 4 6 5 12
N refers to number of subjects; N=6.
Xi refers to the ith person’s score on variable X.
For this data set, X4 = 1, Y 2 = 10.

38. Statistical Notation S Greek letter Sigma symbolizes summation
Subject#
Gender (X)
Age (Y) 1 8 2 10 3 7 4 6 5 12
Gender (x)
Girl
Boy
Y = ?
X = ? 53
Illegal Operation

39. The order of operations is: 1. parentheses 2. exponents
Statistical Notation
Examples 1.3, 1.4 & 1.5 p 28 X X2
(X-1)
(X-1) 2 3 9 2 4 1 7 49 6 36 16
ΣX = = 15
ΣX2 = = 75
Σ(X-1) = = 11
Σ(X-1)2 = = 49
However
ΣX-1 = 15 – 1 = 14
Because
The order of operations is:
1. parentheses
2. exponents
3. multiply / divide
4. summation ( Σ)
5. addition / subtraction

40. Statistical Notation Example 1.6 p 29 ΣX = 3+1+7+4 = 15
ΣY = = 14
ΣXY = = 54
Σ(X + Y) = ΣX + ΣY
Σ(X + Y) = = 29
ΣX + ΣY = = 29
Person X Y XY A 3 5 15 B 1 C 7 4 28 D 2 8