ADV 281 Exam 2: Deck 6

What is this?

Underfitted

What is this?

Good Fit/Robust

What is this?

Overfitted

Correlation measures…

The strength and direction of the relationship between two quantitative variables

Pearson correlation requires:

Two quantitative variables, Paired observations, A meaningful linear relationship, No extreme outliers, Independent observations

Two Quantitative Variables means (For Pearson correlation requirements)

Both variables should be measured at the interval or ratio level

Paired Observations means (For Pearson correlation requirements)

Each participant needs a score on both variables

A Meaningful Linear Relationship means (For Pearson correlation requirements)

The relationship between the two variables should roughly follow a straight line, not a curve

No Extreme Outliers means (For Pearson correlation requirements)

There shouldn’t be any unusual values far from the rest of the data, since one outlier can distort the correlation

Independent Observations means (For Pearson correlation requirements)

Each participant’s scores shouldn’t be influenced by any other participant’s scores

Pearson’s r tells you which two things?

Direction and Strength

Positive correlation (+)

As X increases, Y tends to increase

Negative correlation (−)

As X increases, Y tends to decrease

For Direction, A Pearson’s r near 0 means…

No clear linear relationship

For Strength, a Pearson’s r closer to ±1 means…

A stronger relationship

For Strength, a Pearson’s r closer to 0 means…

A weaker relationship

Which Pearson’s r shows the STRONGEST relationship?

r = −.82

Students who study more hours tend to get higher exam scores. What direction is this correlation?

Positive

Students who spend more hours on TikTok tend to get lower GPAs. What direction is this correlation?

Negative

What Correlation is this?

Perfect Positive Correlation

What Correlation is this?

Zero Correlation

What Correlation is this?

Perfect Negative Correlation

Rules of Thumb for Effect Sizes

0 – .2 = Weak, .3 – .49 = Moderate, > .5 = Strong

In the Rules of Thumb for Effect Sizes, 0 - .2 is:

Weak

In the Rules of Thumb for Effect Sizes, .3 - .49 is:

Moderate

In the Rules of Thumb for Effect Sizes, >.5 is:

Strong

A Pearson’s r of .15 is…

Weak

A Pearson’s r of .42 is…

Moderate

A Pearson’s r of .68 is…

Strong

A Pearson’s r of −.61 is…

A strong negative relationship

The Calculation of r steps

Find how far each person's X score is from the X mean, Find how far each person's Y score is from the Y mean, See whether those deviations tend to point in the same direction or opposite directions, Standardize the result so that the final correlation ranges from −1 to +1.

What question is r basically asking?

Do people who are above average on X also tend to be above average on Y?

If people’s X and Y deviations tend to point in the SAME direction, r will be…

Positive

If people’s X and Y deviations tend to point in OPPOSITE directions, r will be…

Negative

Why is the result standardized at the end?

So the final correlation always ranges from −1 to +1

Students who are above average in hours studied tend to be above average in exam scores. What does this suggest about r?

r is positive

What does this graph show about outliers and Pearson’s r?

One extreme outlier can dramatically change r, making the relationship look weaker (0.4) than it really is without the outlier (0.7)

Test statistic

A number that summarizes the observed data so the statistical test can evaluate the evidence. Its exact meaning depends on the test being used

What question does the test statistic answer?

What pattern did the test detect?

Examples of test statistics

r, t, F, b

The common test statistic for Correlation

r, and often t for testing it

What does a Correlation help evaluate?

The direction and strength of a linear relationship, and whether it differs from zero

The common test statistic for an Independent-samples t-test

t

What does an Independent-samples t-test help evaluate?

How large a difference between group means is relative to its estimated uncertainty

The common test statistic for ANOVA

F

What does ANOVA help evaluate?

How much variation between group means there is relative to variation within groups

The common test statistic for a Chi-square test

χ²

What does a Chi-square test help evaluate?

How much observed categorical data differ from what would be expected under the null hypothesis

Which test uses categorical data?

Chi-square test

What question does the p-value answer?

How surprising are these results under the null hypothesis?

P-value

It tells us how compatible the observed results are with a specified null hypothesis and statistical model

The p-value asks: How likely are we to see THIS data if we assume…

The null hypothesis is true

A p-value is compared to which hypothesis?

The null hypothesis

A study finds r = .35 between influencer credibility and purchase intention, with p = .01. What does the p-value tell us?

These results would be very surprising if there were truly no association in the population

When P < 0.05, it…

Passed

When P > 0.05, it…

Failed

Research question example (Influencer study)

Is perceived influencer credibility associated with consumers’ purchase intentions?

Research hypothesis example (Influencer study)

Perceived influencer credibility is positively associated with purchase intention.

What’s the difference between a research question and a research hypothesis?

A research question asks what you want to find out; a research hypothesis states the answer you predict

Which of the following is a research hypothesis?

“Students who see more TikTok ads will have higher purchase intention.”

What are the two Statistical Hypotheses?

Null Hypothesis and Alternative Hypothesis

Null Hypothesis (H0)

There is no relationship or difference in the population

What is an example of a Null Hypothesis:

There is no association between perceived influencer credibility and purchase intention in the population

Alternative Hypothesis (H1)

There is a relationship or difference in the population

What is an example of a Alternative Hypothesis:

There is a nonzero linear association between perceived influencer credibility and purchase intention in the population

Null hypothesis for a Correlation

The population correlation is zero

Null hypothesis for an Independent-samples t-test

The population means are equal

Null hypothesis for ANOVA

All population group means are equal

Null hypothesis for a Chi-square test of independence

Two categorical variables are independent in the population

“The population means are equal” is the null hypothesis for which test?

Independent-samples t-test

“All population group means are equal” is the null hypothesis for which test?

ANOVA

Two-tailed alternative

There is a relationship or difference, but no direction is specified

Which of the following is an example of a Two-tailed alternative?

“Influencer credibility is associated with purchase intention”

One-tailed alternative

A specific direction is predicted

Which of the following is an example of a One-tailed alternative?

“Higher perceived influencer credibility is associated with higher purchase intention”

Easier way to describe a Two-tailed Alternative Hypothesis

“There’s a relationship, but I’m not saying which way”

Easier way to describe a One-tailed Alternative Hypothesis

“There’s a relationship, and I’m predicting which way”

A statistical test compares…

The observed data with what we would expect under the null hypothesis

In a statistical test, we evaluate…

How compatible the observed data are with the null hypothesis

P value tells us:

Assuming the null hypothesis is true, what is the likelihood that your results happened by chance

Type I error

Rejecting the null hypothesis when it is actually true (false positive)

Type II error

Failing to reject the null hypothesis when it is false (false negative)

A Type I error is also called a…

False Positive

A Type II error is also called a…

False negative

The probability of a Type I error is controlled by…

The significance level, alpha (α)

The probability of a Type II error is commonly represented by…

Beta (β)

Which of the following is an example of a Type I error:

A researcher concludes influencer credibility is associated with purchase intention, but in the population there’s actually no association

Which of the following is an example of a Type II error:

A researcher fails to detect a real association between influencer credibility and purchase intention

A study concludes that a new energy drink ad increases sales, but in reality it has no effect. What is this?

Type I error (false positive)

An ad really does increase sales, but the study finds no significant effect. What is this?

Type II error (false negative)

What size effect does this t-test graph show?

A small effect, since the two groups overlap 92%

Effect size

It describes the magnitude of the result, such as how strongly two variables are associated or how far apart two groups are

Effect size asks…

How strong or large is the relationship or difference?

Study A: n = 40, r = .45, may not reach .05. Study B: n = 1,000, r = .10, may reach .05. What does this show?

A statistically significant result isn’t always a strong one. Study B may pass because of its huge sample, even though its effect is weak.

In the example, which study has the stronger relationship?

Study A (r = .45, moderate)

What does this show?

No Relationship

What does this show?

A Moderate Positive Relationship

What does this show?

A Strong Positive Relationship

What does this show?

A Perfect Positive Relationship

What does this power analysis graph show?

The smaller the effect size, the larger the sample size needed to detect it