19 Apr 2012

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Chapter 8: Hypothesis Testing and Inferential Statistics

Random error: any pattern of data that might have been caused by a true relationship between variables might instead

have been caused by change

Hypothesis Testing Flow Chart

1. Develop research hypothesis

2. Set alpha

3. Calculate power to determine the sample size that is needed

4. Collect data

5. Calculate statistic and p-value

6. Compare p-value to alpha

7. Decide to reject or accept the null

Inferential statistics: use the sample data to draw inferences about the true state of affairs

Sampling distribution: the distribution of all the possible values

Binomial distribution: sample distribution for events have two equally likely possibilities

Null hypothesis: the assumption that the observed data reflect only what would be expected under the sampling

distribution

Significance level (alpha): standard that the observed data must meet

- The smaller the alpha is, the more stringent the standard is

Probability value (p-value): shows the likelihood of an observed statistic occurring on the basis of the sampling

distribution

Two-sided p-values: take into consideration that unusual outcomes may occur in more than one way

- Allow us to interpret statistically significant relationships even if those differences are not in the direction

predicted by the research hypothesis

Type 1 error: when we reject the null, when in fact it is true

- Probability of making a type 1 error = alpha

- The researcher never knows for sure whether she or he has made a type 1 error

- Setting lower alpha protects from Type 1 errors, but doing so may lead us to miss the presence of weak

relationships

Type 2 error: the mistake of failing to reject the null hypothesis when the null hypothesis is really false

- The probability of making a type 2 error = 1-beta

- Type 2 errors are more common when the power of a statistical test is low

Effect size: measures the magnitude of a relationship

- Small = .10, medium = .3 and large = .5

Statistical significance = effect size X sample size

- Increasing sample size will increase the statistical significance of a relationship whenever the effect size if greater

than zero

- Because the p=value is influenced by sample size, as a measure of statistical significance the p-value is not itself a

good indicator of the size of the relationship

- Effect size is an index of the strength of a relationship that is not influenced by sample size

Proportion of explained variability: dependent variable is indicated by the square of the effect-size statistic

Chapter 9: Correlational Research Designs

Scatter plot: uses a standard coordinate system in which the horizontal axis indicated the scores on the predictor variable

and the vertical axis represents the scores on the outcome variable

Regression line: also known as the line of best fit because it is the line that minimizes the squared distance of the points

from the line

Linear relationships: association between the variables on the scatterplot can be easily approximated with a straight line

(positive and linear relationships)

Independent variables: means that we cannot use one variable to predict the other

Curvilinear relationships: relationships that change in direction and this are not described by a single straight line

Coefficient of determination: the proportion of variance measure for r is r2

- When it is not statistically significant, this indicates that there is not a positive or negative linear relationship

between the variables

- However, a non-significant r does not necessarily mean that there is no systematic relationship between the

variables

- Ie/ does not provide a good estimate of the extent of how one variable predicts the other

Chi-squared statistic: must be used to assess the relationship between two nominal variables

Contingency table: to calculate x2 you must construct a contingency table – which displays the number of individuals in

each of the combinations of the two nominal variables

Correlation matrix: a table showing the correlations of many variables with each other

Multiple Regression: a statistical technique based on Pearson correlation coefficients both between each of the predictor

variables and the outcome variable and among the predictor variables themselves

- Requires an extensive set of calculations

- Shows statistics that indicate the relationship between each of the predictor variables and the outcome variable

o Known as regression coefficients or beta weights and their interpretation is very similar to that of r

o Can both be tested for statistical significance

- Multiple correlation coefficient: symbolized by the letter R

o The ability of all of the predictor variables together to predict the outcome variable

Common-causal variable: sometimes known as a third variable

- Another possible explanation for the observed correlation

Spurious relationship: the common-causal variable produces and “explains away” the relationship between the predictor

and outcome variables

Extraneous variables: variables other than the predictor variable that cause the outcome variable but that do not cause

the predictor variable

- Can lead to Type 2 errors

Mediating variable or mediator: a type of variable that can appear in a correlational research design and that is relevant

for gaining a full understanding of the causal relationships among measured variables

Longitudinal research designs: those in which the same individuals are measured more than one time and the time period

between the measurements is long enough that changes in the variables of interest could occur

- Can be used when experimental research is not possible because the predict variables cannot be manipulated

Cross-sectional research designs: are very limited in their ability to rule out reverse causation

- Measure people from different age groups at the same time

Structural equation analysis: a statistical procedure that tests whether the observed relationships among a set of

variables conform to a theoretical prediction about how those variables should be causally related

Latent variables: in a structural equation analysis, and the analysis is designed to assess both the relationships between

the measured and the conceptual variables and the relationships among the conceptual variables

Chapter 10: Experimental Research: One-Way Designs

Experimental manipulations: the researcher can rule out the possibility that the relationship between the independent

and dependent variables is spurious

One-way experimental designs: has one independent variable

Levels: refers to the specific situations that are created within the manipulation (frequently called conditions)

Between-participants design: equivalence can be created either through using different but equivalent participants in

each level of the experiment

Repeated measures design: using the same people in each of the experimental conditions

Experimental condition: the level in which the situation of interest was created

Control condition: level in which the situation was not created

Analysis of Variance (ANOVA): determines if there is an association between the independent and the dependent variable

- Designed to compare the means of the dependent variable across the levels of an experiment research design

Between-groups variance: the variance among the condition means

Within-groups variance: the variance within the conditions