Psychology: Hypothesis Testing

• Research Methods in Psychology is about Hypothesis Testing
• Dr Yang Yap, PhD, from the School of Health and Biomedical Sciences at RMIT

Acknowledgement of Country

• RMIT University recognizes the Woi wurrung and Boon wurrung people of the eastern Kulin Nation, on whose unceded lands the university conducts its business
• RMIT University acknowledges Ancestors and Elders, past and present
• RMIT also acknowledges Traditional Custodians and Ancestors of the lands and waters across Australia where the university conducts its business
• The artwork "Luwaytini" is by Mark Cleaver, Palawa

Learning Objectives

• Understanding the importance of aims and hypotheses is key
• Learning the features of a good hypothesis is important
• Null Significance Hypothesis Testing should be understood
• The Central Limit Theorem should be described and explained
• You should be able to distinguish Descriptive vs Inferential Statistics

Aims & Hypothesis

• Good research aims come from a systematic and an unbiased approach
• A good research aim comes from having a strong understanding of the research design, procedure, statistics, results, and interpretation
• These approaches help researchers to identify gaps in the literature to conduct research, thus forming a research aim
• Research aims provides the overall goal of the research study
• Research aims are usually a general statement

Aim Examples

• Aim examples includes determining whether coping strategy use predicts emotional reactivity
• Examines associations between 24-h sleep-wake behaviors and both valence and arousal dimensions of affect
• To examine the bi-directional, temporal associations between daily stress and sleep across 12 days, using both objective actigraphic and self-report

Hypothesis

• Hypotheses are an educated guess/assumption of a phenomenon
• Hypotheses Propose the possible direction/relationship/outcome between the IV and DV
• Hypotheses help to test/verify theories
• Hypotheses provide information for the types of statistical analyses

Good Hypothesis

• A good hypothesis should be based on prior research and/or theory
• A good hypothesis should be a statement (not question!)
• A good hypothesis should be empirically testable
• A good hypothesis should be specific and operationalised
• A good hypothesis should provide a direction (if possible)

Hypothesis Examples

• it was hypothesised that individuals using higher levels of avoidance-oriented coping strategies (specifically behavioural disengagement, mental disengagement, denial) would have higher levels of NA and PA reactivity to daily stressors
• Individuals using higher levels of approach-oriented coping (specifically active planning, emotional expression, emotional processing, positive reappraisal, acceptance) would have lower levels of NA and PA reactivity to daily stressors.
• (1) Higher evening stress would predict shorter sleep duration (TST) and worse sleep continuity (i.e. longer SOL, higher wake after sleep onset [WASO], and lower SE [22]) on the same night
• (2) Shorter sleep duration and worse sleep continuity would predict higher next-day stress.

Null Significance Hypothesis Testing

• It is a statistical method by which an experimental factor is tested against a hypothesis of no effect, or no relationship based on a given observation
• It has two main competing possibilities:
  • Null hypothesis, denoted as Ho
  • Alternative hypothesis, denoted as H₁

Null Significance Hypothesis Testing (NSHT)

• Null hypothesis, denoted as Ho, assumes the null hypothesis is true
• NSHT essentially proposes that a sample's statistic is not different from the population's statistic
• NSHT proposes that any differences seen in a sample's statistics are simply due to chance (i.e., sample error)
• Alternative hypothesis, denoted as H₁, this proposes that a sample's statistic is different from the population's statistic
• Alternative hypothesis proposes that any differences are not due to chance (i.e., sample error)

Null Significance Hypothesis Testing – Sampling Error

• Given that making inferences about the population is based on the sample, there is going to be sampling error
• Sampling error does not necessarily mean that someone made an error
• This is the random variability of the error
• The difference between the estimates between a sample vs the population
• I.e., the difference between the sample average values vs the population average values
• This error is unavoidable, unless data is collected from the whole population
• Sampling error can be estimated (e.g., margin of error)
• Smaller samples have a greater likelihood of sampling error
• Collecting larger samples can help reduce sampling error
  • The law of large numbers – the larger the sample size, the closer the sample statistic equate to the population statistic
  • Increasing sample size can be costly
• Sampling design – random approach helps to reduce sampling error

Central Limit Theorem

• Similar to the law of large numbers, the central limit theorem proposes that the distribution of the sample means will approximate a normal distribution as the sample size gets larger, regardless of the population's distribution

Back to NSHT

• There are two competing hypotheses: the null and the alternative
• The main goal is to test and decide which of the two the researcher will reject based on the data and results of the sample
• Questions include: Is there a statistically significant difference?
• Is there a statistically significant correlation?
• Does X significantly predict Y?
• If the null hypothesis is rejected, then the alternative will be accepted
• Aim: Examine the relationship between stress and sleep
  • H₀ = There will be no statistically significant relationship between stress levels and sleep duration
  • H₁ = There will be a statistically significant relationship between stress levels and sleep duration
• Aim: Determine the differences in academic performance between short vs long sleepers
  • H₀ = There will be no statistically significant differences in GPA between individuals who sleep < 6hours and individuals who sleep 7-9 hours
  • H₁ = There will be a statistically significant difference in GPA between individuals who sleep < 6hours and individuals who sleep 7-9 hours

P-values

• The p value is the cut-off value that researchers use to test a hypothesis which is the significance level (also known as alpha value)
• The significance level is the probability of a result occurring due to chance
• Researchers usually use values of 0.05, 0.01, or 0.001 (5%, 1% or 0.10%)
• The most common alpha is when p <0.05
• The smaller the p-value, the greater statistical incompatibility of the data with the null hypothesis
  • The smaller the p-value, the stronger evidence against the null hypothesis
• There is a need to reject the null hypothesis when the p-values are less than the cut-off value (e.g., 0.05, 0.01, or 0.001)
• When conducting inferential tests, it really depends on the researcher to decide the p-value – i.e., 0.05, 0.01, or 0.001
• If the p value is 0.025, it means that there is a 2.5% chance that the results could be random (or due to chance)
• When looking at results, the p-values will determined whether results are significant or not
• In practice, there is no such thing as "more significant." It is either significant or not significant, depending on your alpha level (i.e., .05, .01, or .001)
• significant data tells researchers to reject the null hypothesis (depending on the researcher's set alpha value of 0.05, 0.01, or 0.001)
• This means that the alternative hypothesis can be accepted, noting that there is a statistically significant difference/relationship/prediction

Statistics

• There are two main uses of statistics:
  • To describe the sample based on the data collected which is descriptive statistics
  • To make inferences about the population based on the data collected from the sample which is inferential statistics

Descriptive Statistics

• Provide a summary and features of your data through measures of centrality, frequencies, variances, and graphs
• The features of your data can also provide a quick look on the abnormalities in the data – e.g., outliers, data entry errors, or missing data
• Measures of centrality can be done through such as mean, median, and mode
  • mean (i.e., average)
  • median (i.e., the middle observation; 50th percentile)
  • mode (i.e., the most frequent case)
  • A frequency table displays the variables and number of obervations

Descriptive Statistics : Variance

• 1 SD = 2.1
• If the reading score mean (SD) is 6.4 (2.1)
• This means that 68.2% of the sample scored between 6.4 – 2.1 and 6.4 + 2.1
• Thus 68.2% of the sample scored between 4.3 – 8.5 Graphical representations can display the distribution, and show skewed data

Inferential Statistics

• Testing hypotheses will include inferential statistics
• Inferences about the population will be made from the sample that has been collected
• There are two major groups of inferential statistics
• Group/categorical based statistics - comparing means/averages Correlation or regression based statistics - examining relationships
• Correlation or regression based includes: - Pearson's correlation - Linear regression - Multiple linear regression
• Group/categorical based statistics include: - T-test family - ANOVA