Statistics & Interpretation Terms

Confidence Interval (CI)

A range of plausible values for the true population parameter (like the mean). A 95% CI means if you repeated your study 100 times, about 95 of those confidence intervals would contain the true population value. Example: 95% CI [0.8, 3.8] means the true difference is likely between 0.8 and 3.8 points.

Narrow vs. Wide Confidence Interval

NARROW CI = More precision (you have a good estimate of where the true value is). Example: [6.8, 7.6]. WIDE CI = Less precision (you're less certain about the true value). Example: [4.2, 9.2]. Width is affected by sample size (larger n = narrower CI) and variability (larger SD = wider CI).

P-Value

The probability of getting your result (or more extreme) if there were really no effect in the population. A SMALL p-value (typically p < .05) means your result would be very unlikely if there were no real effect, so you conclude there probably IS a real effect. A LARGE p-value (p > .05) means your result could easily happen by chance.

Statistical Significance

A result is statistically significant when the p-value is less than your chosen threshold (usually .05 in psychology). This means: 'This result is unlikely to be due to random chance alone.' IMPORTANT: Statistical significance does NOT mean the effect is large or importantâ€"just that it's probably not due to chance.

The Golden Rule (CI and Significance)

If a 95% confidence interval for the difference between two groups does NOT include zero, then the result is statistically significant at p < .05. Why? Because if the CI doesn't include zero, it means 'no difference' (zero) is not a plausible value. This is the same as saying the difference is statistically significant.

Effect Size

A measure of HOW BIG the difference is between groups, regardless of whether it's statistically significant. Statistical significance tells you IF there's an effect; effect size tells you HOW BIG the effect is. Common measure: Cohen's d (small ≈ 0.2, medium ≈ 0.5, large ≈ 0.8).

Mean (M)

The average score in a group. Calculated by adding all scores and dividing by the number of participants. Example: If Group A has scores of 5, 7, and 9, the mean is (5+7+9)/3 = 7.

Standard Deviation (SD)

A measure of how spread out the scores are around the mean. A SMALL SD means scores are clustered close together (less variability). A LARGE SD means scores are spread out (more variability). Example: SD = 1.2 means scores are tightly clustered; SD = 8.5 means scores vary widely.

Descriptive Statistics

Statistics that summarize and describe what happened in your specific study with your specific participants. They answer: 'What did we observe in our sample?' Examples: mean, standard deviation, bar graphs. They do NOT tell you if results are generalizable or statistically significant.

Inferential Statistics

Statistics that help you make inferences about a larger population based on your sample data. They answer: 'Is this difference meaningful, or could it just be random chance?' Examples: confidence intervals, p-values, significance tests. Purpose: To determine if results generalize beyond your specific sample.

Cohen's d

A standardized measure of effect size for comparing two means. Interpretation: Small effect = d ≈ 0.2, Medium effect = d ≈ 0.5, Large effect = d ≈ 0.8. Example: d = 0.9 means there's a large difference between groups, even if you don't know the original units of measurement.

Margin of Error (ME)

The amount of uncertainty in your estimate; determines how wide your confidence interval is. For means: ME = (z or t) × (s/√n). For proportions: ME = z* × √[pÌ‚(1âˆ'pÌ‚)/n]. Affected by: sample size (larger n = smaller ME) and variability (larger s = larger ME).

Standard Error (SE)

A measure of how much your sample statistic (like the mean) would vary if you repeated the study many times. Formula: SE = s/√n (standard deviation divided by square root of sample size). Smaller SE = more precise estimate. Components: variability in data (s) and sample size (n).

What Happens to CI as Sample Size Increases?

As sample size (n) increases: The standard error SHRINKS, so the confidence interval gets NARROWER (more precise). You have a better estimate of the true population parameter. Example: With n=20, CI might be [4.2, 9.8]; with n=200, CI might be [6.5, 7.5].

What Happens to CI as Standard Deviation Increases?

As standard deviation (s) increases: The standard error GROWS, so the confidence interval gets WIDER (less precise). There's more uncertainty about the true population parameter. Example: With SD=2, CI might be [6.5, 7.5]; with SD=8, CI might be [4.2, 9.8].

NHST (Null Hypothesis Significance Testing)

A statistical approach that starts by assuming there's NO effect (the null hypothesis). Then asks: 'If there's really no effect, how likely is it to get data this extreme?' If that likelihood (p-value) is very small (< .05), we reject the null hypothesis and conclude there probably IS an effect.

Null Hypothesis

The assumption that there is NO effect, NO difference, or NO relationship in the population. It's the 'nothing is happening' hypothesis. Example: 'Caffeine has no effect on reaction time' or 'The mean difference between groups is zero.' NHST starts by assuming this is true, then tests whether the data contradict it.

Estimation and Precision Approach

A statistical approach that focuses on estimating the SIZE of an effect and how precise that estimate is (using confidence intervals and effect sizes). Instead of asking 'Is there an effect?' (yes/no), it asks 'How BIG is the effect?' This gives you more information than just statistical significance.

NHST vs. Estimation Approach - Similarities

SIMILARITIES: Both use the same underlying data. Both make inferences about populations based on samples. Both involve statistical calculations. DIFFERENCE: NHST asks 'Is there an effect?' (yes/no decision). Estimation asks 'How big is the effect?' (magnitude and precision).

NHST vs. Estimation Approach - Differences

NHST Approach: Question = 'Is there an effect?' (yes/no). Focus = p-value and significance. Answer = Reject or fail to reject null hypothesis. ESTIMATION Approach: Question = 'How big is the effect?' Focus = Effect size and confidence intervals. Answer = Magnitude and precision of the effect.

Direct Replication

Repeating a study using the SAME methods, measures, and procedures to see if you get the same result. Purpose: To verify that the original finding is reliable and not a fluke. Example: If Study 1 found that caffeine improves memory, a direct replication would use the exact same caffeine dose, memory test, and procedure.

Conceptual Replication

Testing the SAME underlying idea or theory but using DIFFERENT methods, measures, or contexts. Purpose: To see if the finding generalizes beyond the specific methods of the original study. Example: If Study 1 found caffeine improves memory using word lists, a conceptual replication might test if caffeine improves memory using face recognition.

Replication-Plus-Extension

First REPEATING the original study (direct replication), then ADDING something new to learn more. Purpose: To verify the original finding AND extend knowledge. Example: First replicate the caffeine-memory study exactly, then add a new condition (like testing different caffeine doses) to see if the effect depends on dose.

Bar Graph with Error Bars

A visual display where bars show the MEAN for each group, and ERROR BARS (lines extending from the top of each bar) show VARIABILITY. Longer error bars = more variability in the data. Error bars can represent standard deviation, standard error, or confidence intervals. Used to visually compare groups.

The Five Steps of Estimation and Precision

1) Define the parameter and question (What are we estimating?). 2) Choose estimator, confidence level, and note assumptions (Usually 95% CI). 3) Collect data and check assumptions (Make sure data meet requirements). 4) Compute point estimate and standard error (Calculate mean difference and uncertainty). 5) Construct and interpret the confidence interval (Build CI and interpret precision).

Point Estimate

A single value that serves as your best guess for a population parameter based on your sample data. Example: If your sample mean is 7.2, that's your point estimate for the population mean. The confidence interval then tells you the range of plausible values around that point estimate.

Population Parameter

The true value in the entire population that you're trying to estimate. Examples: the true population mean, the true difference between groups, the true proportion. You can never know this for certain (unless you measure the entire population), so you use sample statistics to ESTIMATE it.

Sample Statistic

A value calculated from your sample data that you use to estimate a population parameter. Examples: sample mean (M), sample standard deviation (SD), sample proportion. These are what you actually observe in your study, and you use them to make inferences about the population.

Precision (in statistics)

How narrow or wide your confidence interval is. HIGH PRECISION = narrow CI (you have a good estimate of the true value). LOW PRECISION = wide CI (lots of uncertainty about the true value). Precision is improved by: larger sample size and less variability in the data.

Why Use Inferential Statistics Instead of Just Descriptive?

Descriptive statistics only tell you what happened in YOUR specific sample. Inferential statistics let you make conclusions about the LARGER POPULATION based on your sample. Without inferential stats, you can't know if your results would generalize to other people or if they're just a fluke in your particular sample.

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