Marketing Research quiz 3 Part 2

what is a mathematical difference

A mathematical difference just means the numbers are different. It does not automatically mean the difference is important or meaningful.

What is a managerially important difference?

A managerially important difference is a difference large enough to matter to the manager or to affect a business decision.

What is a statistically significant difference?

A statistically significant difference is a difference large enough that it is not likely to have happened because of chance or sampling error.

What is a hypothesis

A hypothesis is a supposition or proposed explanation based on limited evidence that serves as a starting point for investigation.

why should you care for a hypothesis

You should care because hypothesis testing helps prove or disprove assumptions and identify meaningful insights that can guide business strategy.

how do you state hypothesis

Null hypothesis (H0): the status quo (also) Alternative hypothesis (Ha or H1): the hypothesis of interest

Statistical test (Chi Square)

Use chi-square when you have one categorical independent variable and one categorical dependent variable. It is used for nominal or categorical data and checks whether frequencies fit an expected pattern or whether two variables are related.

Statistical test (Independent samples t-test)

Use an independent-samples t-test when you have one categorical independent variable with only 2 groups and one continuous dependent variable measured by mean. It tests whether the two groups differ on a continuous measure.

Statistical test (paired sample t test)

Use a paired-sample t-test when the same respondents provide both measures, such as pre/post designs or rating two different objects. It compares two means from the same sample.

Statistical test (One way ANOVA)

Use one-way ANOVA when you have one categorical independent variable with 2 or more groups and one continuous dependent variable measured by mean. It tests whether the group means differ.

Statistical test (Z-test)

Use a two-proportion z-test when you have one categorical independent variable with 2 groups and a dependent variable measured as a proportion or percentage. It compares proportions between two independent groups.

what is a significance level

A significance level is the cutoff used to decide whether the evidence is strong enough to reject the null hypothesis. It shows how unlikely a result must be before we say it probably did not happen by chance.

What is alpha (α)?

Alpha (α) is the symbol for the significance level. It is the probability considered too low to keep accepting the null hypothesis. Common alpha levels are .10, .05, and .01.

How do you decide whether to reject or fail to reject the null hypothesis?

You compare your test result to the alpha level you chose. If the result is significant enough under that alpha level, you reject H0. If it is not significant enough, you fail to reject H0.

How do you decide on your alpha level?

You decide on your alpha level before testing by choosing the standard you want to use for significance. The slides list .10, .05, and .01 as the common choices.

What is a decision rule?

A decision rule is the standard you set ahead of time that tells you when to reject or fail to reject the null hypothesis.

What does rejection of the null hypothesis mean?

Rejecting the null hypothesis means the evidence supports the alternative hypothesis.

Why is it important to reduce the risk of errors? (what two major mistakes are they)

Type I error: rejecting H0 when it is actually true, which is a false positive

Type II error: failing to reject H0 when it is actually false, which is a false negative

How do sample size, alpha, and confidence intervals affect risk?

Bigger sample size = less sampling error, better chance of finding real differences

Bigger alpha = easier to find significance, but more false positives

Higher confidence level = stricter standard, fewer false positives but harder to find significance

How to read significance testing on a chart

You are looking for whether the difference shown on the chart is marked as statistically significant. That means the difference is unlikely to have happened just by chance.

What does "95% confidence level" mean on the chart?

A 95% confidence level means the result meets the standard for significance at that level. In other words, the difference is strong enough that it is not likely due to random chance.

What test is usually being used for crosstab significance?

For crosstabs with nominal data, the test used is chi-square (χ²).

How is significance usually marked on a crosstab?

Significance is usually marked with letters that refer to other columns. Those letters show which columns are significantly different from each other.

How do you read a crosstab correctly?

The rule from class is to read down the column and back across the row. That helps you compare the group percentages correctly.

What does a significant result on a chart tell you?

It tells you that one group is significantly more or less likely than another group on that measure. It means the difference is probably real, not just random sampling error.