PSY201H1 Comprehensive Guide to t-Statistics and
Hypothesis Testing in Psychology University of
Toronto
Comprehensive Guide to t-Statistics
and Hypothesis Testing in Psychology
Null Hypothesis Significance Testing (NHST)
Null Hypothesis Significance Testing (NHST) is a systematic procedure
used to determine whether observed data provide sufficient evidence to
reject a null hypothesis. The process involves several key steps:
Stating the hypotheses: Formulate the null hypothesis (H0), which
posits no effect or no difference, and the alternative hypothesis (H1),
which suggests an effect or difference.
Creating a decision rule: Decide on a significance level (α), typically
0.05, and determine the critical value(s) from the relevant distribution.
Data collection and test statistic calculation: Collect sample data and
compute the appropriate test statistic (z, t, etc.).
Making a decision: Compare the test statistic to the critical value(s) to
decide whether to reject H0.
, Reporting results: Summarize findings with effect sizes, p-values, and
confidence intervals to convey both statistical and practical
significance.
This framework applies across various tests, including z-tests and t-tests,
and ensures a consistent approach to evaluating hypotheses.
Z-Statistic and Z-Test
The z-test compares a sample mean to a known population mean when
the population variance (σ²) is known. The z-statistic is calculated as:
z = (M - μ) / (σ / √n)
, where:
M = sample mean
μ = population mean
σ = population standard deviation
n = sample size
Key points:
Used when population variance is known.
The distribution of the z-statistic follows the standard normal
distribution.
Significance is determined by comparing the calculated z-value to
critical z-values (e.g., ±1.96 for α=0.05 in two-tailed tests).
Application example: Testing whether listening to music affects cognitive
performance, comparing the sample mean to the known population mean.
Effect Size Measurement
While significance tests indicate whether an effect exists, effect sizes
quantify its magnitude, offering practical insights. Common effect size
measures include:
Cohen's d: Measures the difference between two means in units of
standard deviation:
d = (M1 - M2) / s_pooled
Small effect: d ≈ 0.2
Medium effect: d ≈ 0.5
Large effect: d ≈ 0.8
Coefficient of determination (r²): Represents the proportion of
variance explained by the effect:
Hypothesis Testing in Psychology University of
Toronto
Comprehensive Guide to t-Statistics
and Hypothesis Testing in Psychology
Null Hypothesis Significance Testing (NHST)
Null Hypothesis Significance Testing (NHST) is a systematic procedure
used to determine whether observed data provide sufficient evidence to
reject a null hypothesis. The process involves several key steps:
Stating the hypotheses: Formulate the null hypothesis (H0), which
posits no effect or no difference, and the alternative hypothesis (H1),
which suggests an effect or difference.
Creating a decision rule: Decide on a significance level (α), typically
0.05, and determine the critical value(s) from the relevant distribution.
Data collection and test statistic calculation: Collect sample data and
compute the appropriate test statistic (z, t, etc.).
Making a decision: Compare the test statistic to the critical value(s) to
decide whether to reject H0.
, Reporting results: Summarize findings with effect sizes, p-values, and
confidence intervals to convey both statistical and practical
significance.
This framework applies across various tests, including z-tests and t-tests,
and ensures a consistent approach to evaluating hypotheses.
Z-Statistic and Z-Test
The z-test compares a sample mean to a known population mean when
the population variance (σ²) is known. The z-statistic is calculated as:
z = (M - μ) / (σ / √n)
, where:
M = sample mean
μ = population mean
σ = population standard deviation
n = sample size
Key points:
Used when population variance is known.
The distribution of the z-statistic follows the standard normal
distribution.
Significance is determined by comparing the calculated z-value to
critical z-values (e.g., ±1.96 for α=0.05 in two-tailed tests).
Application example: Testing whether listening to music affects cognitive
performance, comparing the sample mean to the known population mean.
Effect Size Measurement
While significance tests indicate whether an effect exists, effect sizes
quantify its magnitude, offering practical insights. Common effect size
measures include:
Cohen's d: Measures the difference between two means in units of
standard deviation:
d = (M1 - M2) / s_pooled
Small effect: d ≈ 0.2
Medium effect: d ≈ 0.5
Large effect: d ≈ 0.8
Coefficient of determination (r²): Represents the proportion of
variance explained by the effect:
