RESEARCH METHODS

CENTRAL LIMIT THEOREM (CLT)

The distribution of sample means will become approximately normal as sample size increases, regardless of the population’s shape. (This explains why many statistical tests work even when sample data distributions are not perfectly normal.)

COHEN’S D

A measure of effect size expressing the mean difference in standard deviation units.
CALCULATED BY: Subtract one mean from the other, then divide by the standard deviation (for paired samples, use the SD of the difference scores).

• 0.2 is small

• 0.5 is medium

• 0.8 or higher is large

CONFIDENCE INTERVAL (CI)

• provides a range of values that is likely to contain the true population parameter (e.g., mean difference, correlation) with a certain level of confidence, usually 95%.

• width indicates precision, narrower intervals mean more precise estimates

• provide more information than a single p-value because they show both the direction and the plausible size of the effect

CALCULATE : Use the sample estimate ± (critical value × standard error).

DISTRIBUTION OF SAMPLE MEANS

• distribution formed by the means of many random samples of the same size from a population

• approximately normal due to the central limit theorem

STANDARD ERROR

• standard deviation of the distribution of sample means

• sample size INCREASE → standard error DECREASE

• MEANING the estimation of the population mean becomes more precise

EFFECT SIZE

describes the magnitude or strength of a relationship, difference, or effect in a study (independent of sample sizes)

• COHEN’S D is an effect size

INTERQUARTILE RANGE (IQR)

The range within which the middle 50% of the scores fall

CALCULATE : Find the 25th percentile (Q1) and 75th percentile (Q3), then subtract Q1 from Q3.

LAW OF LARGE NUMBERS

As sample size increases, the sample mean gets closer to the true population mean, making estimates more accurate.

EXPERIMENTAL HYPOTHESIS (H₁)

statement that predicts an effect (of difference or association)

also called alternative hypotheses (alternative to the NULL HYPOTHESIS)

NULL HYPOTHESIS (H₀)

• predicts that there will be no effect, difference, or relationship in the population

• statistical tests assess whether there is enough evidence to reject it (p value)

• SMALL VALUE (< 0.5) suggests that results are under the H₀, reject H₀ (ALTERNATIVE TRUE)

• LARGE VALUE suggests that data is consistent with H₀. do not reject (NULL TRUE)

P VALUE (p)

• the p value is the probability of obtaining results at least as extreme as those observed in a sample, if the null hypothesis (H₀) were true

• SMALL VALUE (< 0.5) suggests that results are under the H₀, reject H₀ (ALTERNATIVE TRUE)

• LARGE VALUE suggests that data is consistent with H₀. do not reject (NULL TRUE)

PEARSON CORRELATION ( r )

• measures the strength and direction of the linear relationship between two variables (x and y)

• values between -1 and 1

• the SIZE of R represents how close the data is to a straight line (closer to 1 = straighter line)

• the SIGN ( - or + ) specifies the direction of the association

CALCULATE : Compare how scores on one variable change with scores on another variable

• 0.10 weak (small effect)

• 0.30 moderate (medium effect)

• 0.50 high strong (large effect)

PROBABILITY

likelihood that a particular outcome will occur, expressed as a number between 0 (impossible) and 1 (certain).

SAMPLE

subset of the population that is observed or measured in a study. Samples are used to infer conclusions about populations.

STANDARD DEVIATION (SD)

measure of how spread out scores are around the mean

STANDARD ERROR (SE) FOR z-test

estimate of how much the sample mean is likely to vary from the population mean.

CALCULATE : Divide the standard deviation by the square root of the sample size.

STANDARD ERROR (SE) FOR t-test

estimate of how much the sample mean is likely to vary from the population mean.

SM = sample mean

S = sample standard deviation

n = sample size

T SCORE (t)

statistic used to test whether two means differ significantly

CALCULATE : Subtract one mean from the other, then divide by the standard error of the difference

• the alpha level will not be fixed at ±1.96 like in a t-test

INDEPENDENT GROUPS RESEARCH DESIGN

participants are assigned to 2 or more different groups

DEGREES OF FREEDOM (df)

one less than the sample (n-1)

Z SCORE (z)

• expresses how many standard errors our sample mean is away from H₀

CALCULATE : (single sample z-test) Subtract the mean from the score, then divide by the standard deviation.

• E.G. z score = 1.5 (sample mean is 1.5 standard errors above the mean)

FORMULA

• z = z-score for sample mean

• M = sample mean

• u = population mean

• oM = standard error of the mean

NORMAL DISTRIBUTION

95% of scores within 2 standard deviations of the mean (these scores are typical)

5% of scores outside of 2 standard deviations of the mean (these scores are extreme)

ALPHA LEVEL

• AKA level of significance

• 5%

• defines which sample means in a distribution are typical if the null hypothesis is true

• in a NORMAL DISTRIBUTION = ±1.96

• IF the sample mean is WITHIN these limits = do not reject H₀

• IF sample mean is OUTSIDE these limits = reject H₀

CORRELATION

examining the relationship between 2 variables

• no control or manipulation

• positive linear association : line goes up

• negative linear association : line goes down