Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 9: Introduction to the t Statistic, Chapter 14: Correlation and…
Chapter 9: Introduction to the t Statistic
Used when
population standard deviation (σ)
is unknown.
Allows hypothesis testing using sample data
Often used in small sample studies
Hypothesis Testing with t
Process
:
1
. State hypothesis,
2
. Set alpha level (e.g., 0.05),
3
. Compute t statistic,
4
. Determine critical t value from t table,
5
. Compare and conclude
Effect Size (Cohen's d)
: Measures magnitude of treatment effect
Effect Size (Cohen's d formula: d = M-μ/s
Estimated Standard Error (SE)
: Measure of how much difference to expect between two variables
SE= sM=8/n: s is the sample deviation; n is the sample size
t Statistic Formula: t= M-u/sM
Degrees of Freedom
(df):Compares sample mean M to population mean μ using estimated standard error.
Degrees of Freedom formula: df = n-1
t-Distribution
: Siimilar to normal distribution
Flatter and
more spread
out than the normal curve, especially with smaller samples.
Approaches normality as n increases
Assumptions of the
t
Test
: Values in the sample must consist of independent observations
t
Distribution vs Normal Distribution
: Greater variability (larger tails) With larger
df
,
t
distribution approaches a normal shape
Chapter 14: Correlation and Regression
Used to measure and describe the relationship between two variables
Helpful in prediction, understanding relationships and identifying trends
Pearson Correlation (r)
: Measures linear relationship between two interval or ratio variables
Pearson (r) formula: r = cov (X, Y)/sXsY
Interpretation: Values range from
-1.00 to +1.00
;
+1
= positive correlation,
-1
= negative correlation,
0
= no correlation
Strength of Correlation:
0.1-0.3
: weak,
0.3-0.5
: moderate,
0.5
: strong
Direction:
Positive r
: AS X increases, Y increases
Negative r:
As X increases, Y decreases
Correlation
does not imply causation
Outliers can distort correlation
Only appropriate for
linear
relationships
Coefficient of Determination
: Represents the proportion of variance in on variable that is predictable from the other
r2= shared variance (e.g. r = 0.70, then r2 = 0.49, so 49% of the variance is shared
Point-Biserial
: When one variable is dichotomous or divided into distinct parts and the other is lineari
Phi coefficient (φ)
: When both variables are dichotomous
Standard Error of Estimate
: Measures how accurately the regression line prediction of actual Y Scores
Linearity
: Change in one variable corresponds to a proportional change in another
Normally
distributed variables (for inference)
Formula
(simple regression) SE ∑ (Y− Y^) 2/ n-2
Homoscedasticity
: Equal spread of data points across regression line
Assumptions in Correlation and Regression
Linear Regression
: Predicts Y from X using the line of best fit
Regression Equation
: Y= bX+a
b = slope = SP/SSx; a = Y-intercept = M
y
-bM
x
SP = sum of products of deviations; SS_X = sum of squares for X
Spearman Correlation
(ρ or rₛ): Used for ordinal data or non-linear but unchanged relationships