Clever Grades

🎧 Read Aloud

Inferential Statistics

Foundations of Inference

Drawing Conclusions

Inferential statistics allow psychologists to draw conclusions from sample data about a larger population. These statistics involve hypothesis testing, probability, and specific statistical tests based on assumptions and data type.

Distribution Curves

🔔

Normal Distribution

A normal distribution is a symmetrical, bell-shaped curve centered on the mean. Mean = median = mode in a perfect normal distribution. Percentages of data lie within standard deviations from the mean: about 68% within ±1 SD, 95% within ±2 SD, and 99.7% within ±3 SD (the empirical rule).
⇶

Skewed Distribution

Skewed distributions are asymmetrical, with a long tail on one side. Positive skew: tail on the right, most values on the left. Negative skew: tail on the left, majority on the right. Skewness affects measures of central tendency (mean is pulled toward the tail).

Probability and Significance

Understanding how likely our findings are due to chance is the core of statistical inference.

P

Probability

Probability (p) is the likelihood an event will happen, ranging from 0 (impossible) to 1 (certain). In hypothesis testing, it represents the chance results are due to random variation rather than a true effect.
α

Significance Levels

The significance level (alpha) is the threshold set before the test, often .05. Results yielding p < alpha reject the null hypothesis (no effect). Alpha levels can be adjusted for more stringent tests (.01 or .001).

Critical Values

📚

Using Statistical Tables of Critical Values: Statistical tables provide critical values against which calculated test statistics are compared. If the test statistic exceeds the critical value, results are significant. Critical values depend on alpha, degrees of freedom (df), and the test type.

Parametric Test Criteria

Parametric tests assume specific data properties. If these criteria are not met, non-parametric tests are preferred.

1

Data Level

Interval or ratio level data.
2

Distribution

Normally distributed populations or large enough sample sizes (Central Limit Theorem).
3

Variance

Homogeneity of variance: similar variance across groups.
4

Observations

Independent observations.

Specific Non-Parametric Tests

Each test has assumptions related to data type and independence, analyzing ranks or frequencies instead of means.

U

Mann-Whitney U test

For comparing two independent groups when data are ordinal or not normally distributed.
W

Wilcoxon Signed Ranks test

For comparing two related groups (matched pairs or repeated measures) with ordinal or non-normal data.
χ²

Chi-square test

For testing relationships between two nominal variables and to evaluate goodness-of-fit.
B

Binomial Sign test

For testing directional hypotheses with nominal data, often used with small sample sizes or paired nominal data.
ρ

Spearman's Rho

To assess correlation between two ordinal variables or non-normally distributed interval data.

Risk of Error

⚠️
Type 1 Error (False Positive)Rejecting the null hypothesis when it is actually true. For example, concluding a treatment works when it does not. Probability is alpha (usually 5%).
🛑
Type 2 Error (False Negative)Failing to reject the null hypothesis when the alternative hypothesis is true. Missing a real effect. Probability is beta.

Statistical Notation Symbols

=

=

equals.
<

<

less than.
<<

<<

much less than.
>

>

greater than.
>>

>>

much greater than.
x

x

multiplication or test statistic symbol.
~

~

approximately equal to.
Inferential Statistics Deck
Term
Inferential Statistics

What is inferential statistics?

Answer
Definition

Drawing conclusions about a population based on sample data.

Term
Normal Distribution Curve

What shape defines a normal distribution curve?

Answer
Definition

A symmetrical, bell-shaped curve centered on the mean.

Term
±1 Standard Deviation

What percentage of data lies within ±1 standard deviation in a normal distribution?

Answer
Approximate Value

Approximately 68%.

Term
Positive Skew

What does a positive skew indicate in a distribution?

Answer
Description

A long tail on the right with most values on the left.

Term
Statistical Significance

What is the general threshold for statistical significance (p-value)?

Answer
Threshold

p < .05.

Term
Significance Level (Alpha)

What does the significance level (alpha) represent?

Answer
Definition

The threshold for rejecting the null hypothesis, often set at .05.

Term
Parametric Tests

When are parametric tests appropriate to use?

Answer
Conditions

When data are interval/ratio, normally distributed, variances are equal, and observations are independent.

Term
Mann-Whitney U Test

Which non-parametric test compares two independent groups with ordinal or non-normal data?

Answer
Test Type

Mann-Whitney U test.

Term
Type 1 Error

What is a Type 1 error?

Answer
Definition

Rejecting the null hypothesis when it is true (false positive).

Term
Less Than Symbol

What symbol is commonly used to indicate "less than"?

Answer
Symbol

<

Tip: Tap a card to flip. Shuffle or Reset anytime.

📊 Statistics & Hypothesis Testing Quiz

1. What does a p-value less than 0.05 typically indicate?

A p-value < 0.05 shows that the findings are unlikely to have occurred by chance.

2. Which test is appropriate for comparing two related groups with ordinal data?

Wilcoxon Signed Ranks test is used for two related groups with ordinal or non-normal data.

3. In a perfectly normal distribution, which of the following is true?

In a normal distribution, the three measures of central tendency are equal.

4. Which type of error occurs when the null hypothesis is wrongly rejected?

Type 1 error is a false positive, rejecting a true null hypothesis.

5. Which of these is NOT an assumption for parametric tests?

Parametric tests require interval/ratio level data; nominal data is for non-parametric tests.

📊 Results

  • Notes and Quiz
  • Psychology
  • A Level
  • Stress
  • OCR