# PSYCH 100A Lecture Notes - Lecture 7: Null Hypothesis, Analysis Of Variance, Scatter Plot

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Published on 28 Mar 2018

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Lecture 7

If the population means are identical (null is true), the probability of drawing a sample that

gives an F of 7.41 or larger is 0.008 (8 out of 1000)

• P values less that 0.05 (p <0.05) provide evidence against the null hypothesis

• Results were significant, meaning that at least one group average differs from the others

Significant F Test

• ANOVA null hypothesis - predicts that all population means are equal

• A significant F statistic implies that at least one pair of groups is different

o With more than two groups, a significant F is ambiguous because we don't know

which pairs of groups is driving the significant result

Pairwise (post hoc) comparisons

• Examine mean differences between all possible pairs of groups

• Used when researches don't have specific hypotheses about group differences prior to

study

Idea that two events tend to happen together

• Correlation (r )describes associations/trends between two continuous variables

Use correlation:

• T tests apply to situations where we want to examine relationship between categorical

independent variable and continuous dependent variable

• But correlation used to evaluate association between two continuous variables

Scatterplot

• Helps visualize a correlation

• Independent on horizontal, outcome on vertical

• Correlation differs in direction and strength

o Can be positive or negative

o Strength of correlation ranges from weak (nonexistent) to strong (perfect)

Positive correlation

• High paired with high, low paired with low

Negative correlation

• High paired with low, low paired with high

Pearson's Correlation

• Denoted r

o Quantifies magnitude of correlation on a 0 to 1 scale

o Slope of the line

Not a percentage, not a ratio scale

• Correlation of 0.30 not twice as strong as 0.15

• Correlation does not imply causation

o Zero correlation may/may not imply lack of association

o Can't quantify nonlinear relations

• No correlation DOES NOT mean independent or unrelated variables

• There are nonlinear relationships

Outliers (extreme scores)

find more resources at oneclass.com

find more resources at oneclass.com

## Document Summary

Pairwise (post hoc) comparisons: examine mean differences between all possible pairs of groups, used when researches don"t have specific hypotheses about group differences prior to study. Idea that two events tend to happen together: correlation (r )describes associations/trends between two continuous variables. Use correlation: t tests apply to situations where we want to examine relationship between categorical independent variable and continuous dependent variable, but correlation used to evaluate association between two continuous variables. Scatterplot: helps visualize a correlation, correlation differs in direction and strength. Independent on horizontal, outcome on vertical: can be positive or negative, strength of correlation ranges from weak (nonexistent) to strong (perfect) Positive correlation: high paired with high, low paired with low. Negative correlation: high paired with low, low paired with high. Pearson"s correlation: denoted r, quantifies magnitude of correlation on a 0 to 1 scale, slope of the line. Outliers (extreme scores: have substantial impact on correlation, can increase/decrease depending on location of outlier.