Data Analysis for Marketing Decisions

A prediction about how something works in the real world.

The opposite of the alternative hypothesis. It states that no effect exists.

Statistical testing aims to collect enough evidence to reject the null hypothesis.

Failing to find enough evidence to reject the null hypothesis.

The process of calculating how likely it is to observe your data, assuming the null hypothesis is true.

The statistical likelihood of observing your data, assuming the null hypothesis is true.

A specific value that defines the boundary between rejecting or failing to reject the null hypothesis.

The process of making a decision about the null hypothesis based on the p-value and significance level.

The probability of making a Type I error. This occurs when we reject the null hypothesis (H0) when it is actually true, leading to a false positive conclusion. In other words, we conclude that there is an effect when there is none.

The probability of making a Type II error, which happens when we fail to reject the null hypothesis when it is actually false. This results in a false negative conclusion, meaning we miss a real effect.

Represents the situation where we correctly fail to reject the null hypothesis, indicating no significant effect.

Represents the situation where we correctly reject the null hypothesis, indicating a significant effect.

A measure of how frequently different results occur under the assumption that the null hypothesis is true.

A specific value from the test statistic's distribution that divides the rejection region from the non-rejection region.

The process of determining if your data provides enough evidence to reject the null hypothesis.

A standardized measure of the size of an effect.

Indicates a small, medium, or large effect size.

Measures the strength and direction of the linear relationship between two variables.

The practice of comparing effect sizes from different studies.

The probability of obtaining a test statistic (or bigger) if the null hypothesis is true.

The predetermined threshold for rejecting or failing to reject the null hypothesis. It's typically set at 0.05.

Rejecting the null hypothesis when it is actually true, resulting in a false positive conclusion.

Failing to reject the null hypothesis when it is actually false, leading to a false negative conclusion.

A statistical approach used to determine whether there is enough evidence to reject a null hypothesis.

The direction of the anticipated effect. For example, a prediction of a positive or negative relationship between two variables.

A hypothesis that does not specify the direction of the effect. It simply predicts the existence of a relationship between variables.

The process of comparing the obtained test statistic to a critical value determined by the significance level to decide whether to reject the null hypothesis.

In hypothesis testing, we aim to either reject or fail to reject the null hypothesis (H0). The decision is based on whether the confidence interval for the sample mean contains the value specified by the null hypothesis. If the confidence interval includes the H0 value, we fail to reject the null hypothesis. On the other hand, if the confidence interval does not include the H0 value, we reject the null hypothesis in favor of the alternative hypothesis (H1).

The confidence interval (CI) provides a range of plausible values for the population mean based on the sample data. This range is constructed with a specific confidence level, typically 95%, which means that if we were to repeat the sampling process many times, 95% of the CIs would contain the true population mean.

The width of the confidence interval is determined by the confidence level and the variability of the data. A higher confidence level leads to a wider interval, while lower variability (smaller standard deviation) results in a narrower interval.

When comparing two samples, the confidence intervals can overlap. The degree of overlap indicates the strength of evidence against the null hypothesis. Moderate overlap (≤50%) suggests that the difference between the two samples is not significant. Conversely, if the confidence intervals show little or no overlap, it suggests a more significant difference.

The p-value represents the probability of observing the data we have collected, assuming the null hypothesis is true. A smaller p-value (less than the significance level, α) indicates that the observed data is highly unlikely to occur if the null hypothesis is true. This provides stronger evidence against the null hypothesis. Conversely, a larger p-value suggests that the data is more likely to occur under the null hypothesis and weakens the evidence against it.

A Type I error occurs when we reject the null hypothesis when it is actually true. It is considered a false positive error. In other words, we conclude that there is an effect when there is none in reality. The probability of making a Type I error is represented by the significance level (α).

A Type II error occurs when we fail to reject the null hypothesis when it is actually false. It is considered a false negative error. This means we miss a real effect that exists. The probability of making a Type II error is represented by β (beta).