7.5.2.3 Reporting Psychological Investigations

• A hypothesis is a testable statement that predicts the outcome of a research study
• What are the two main types of hypotheses?

  Directional and Non-Directional
• A directional hypothesis states the specific direction of the effect.
• A non-directional hypothesis states there will be a difference but does not specify the direction
• What does the null hypothesis state?

  No effect or relationship
• Steps in choosing an inferential statistical test

  1️⃣ Determine the level of measurement

  2️⃣ Identify the research design

  3️⃣ Check data assumptions
• What is nominal data?

  Categories without order
• Ordinal data consists of ordered categories
• Interval/Ratio data includes continuous data with equal intervals.
• Match the statistical test with its corresponding level of measurement and research design:

  t-Test ↔️ Interval/Ratio, Independent Groups

  Paired t-Test ↔️ Interval/Ratio, Repeated Measures

  Chi-Square ↔️ Nominal, Groups

  Mann-Whitney U ↔️ Ordinal, Independent Groups
• Why is it vital to check data assumptions when choosing a statistical test?

  To ensure valid results
• The null hypothesis states that there is no effect or relationship.
• The first factor in choosing an inferential statistical test is the level of measurement
• What are the main levels of measurement in statistics?

  Nominal, Ordinal, Interval/Ratio
• Research designs include Independent Groups, Repeated Measures, and Correlational
• Normality is a key data assumption in inferential statistics.
• Which statistical test requires the assumption of homogeneity of variance?

  t-Test
• The paired t-Test requires the data to be normal
• The Chi-Square test requires a large sample size.
• Which statistical test does not require any data assumptions?

  Mann-Whitney U
• The Spearman's Rho test is used with data at the ordinal
• Which statistical test is used with interval/ratio data and requires normality?

  Pearson's r
• Steps in calculating a test statistic

  1️⃣ Collect data

  2️⃣ Choose a test statistic

  3️⃣ Calculate the statistic

  4️⃣ Interpret the result
• A test statistic is a numerical value calculated from sample data to measure the extent to which it supports or contradicts the null hypothesis
• What is the formula for the t-statistic?

  $t =$ \frac{\bar{x}_{1} - \bar{x}_{2}}{s_{p}\sqrt{\frac{1}{n_{1}} + \frac{1}{n_{2}}}}
• The Chi-Square statistic assesses goodness-of-fit or independence.
• The Chi-Square statistic is used to analyze categorical data.
• The formula for the Chi-Square statistic is \chi^{2} = \sum \frac{(O - E)^{2}}{E}</latex>
• What does a test statistic measure?

  Statistical significance
• Steps in the general process of using a test statistic

  1️⃣ Collect data

  2️⃣ Choose a test statistic

  3️⃣ Calculate the statistic

  4️⃣ Interpret the result
• The t-statistic is used to compare means of two groups.
• In the t-statistic formula, $\bar{x}_{1}$ and $\bar{x}_{2}$ represent the sample means.
• What type of data does the Chi-Square statistic analyze?

  Categorical
• A p-value is the probability of obtaining results as extreme as or more extreme than the observed data, assuming the null hypothesis is true.
• A directional hypothesis states the specific direction of the effect.
• What does the null hypothesis state?

  No effect or relationship
• Steps in the general process of using a test statistic

  1️⃣ Collect data

  2️⃣ Choose a test statistic

  3️⃣ Calculate the statistic

  4️⃣ Interpret the result
• A p-value is the probability of obtaining results more extreme than the observed data, assuming the null hypothesis is true.
• What is the typical significance threshold used for p-values?

  0.05
• If the p-value is less than or equal to the significance threshold, the null hypothesis is rejected.