ASSESSMENT UPDATE ANOVA TTEST ETC

In a normal distribution, what is the relationship between mean, median, and mode?

A: Mean = Median = Mode

What percent of scores fall within 1 standard deviation in a normal curve?

68

What percent of scores fall within 2 standard deviations?

95

What percent of scores fall within 3 standard deviations?

99

What does standard deviation measure?

How spread out scores are from the mean.

What does ±1 Standard Deviation mean?

It means you go:

1 SD BELOW the mean
and
1 SD ABOVE the mean

Step-by-step with your numbers:

Mean = 100
Standard Deviation (SD) = 10

Lower end (−1 SD)

Mean − SD
= 100 − 10
= 90

2⃣ Upper end (+1 SD)

Mean + SD
= 100 + 10
= 110

So:

±1 SD range = 90 to 110

🧠 What does this tell us?

In a normal distribution:

👉 68% of all scores fall between 90 and 110

What is ±2 SD?
If the mean is 100 and SD is 10?

When the mode and median are higher than the mean, it is a ______ skew.

Negative skew

When the mode and median are lower than the mean, it is a ______ skew

positive skew

mean is just the average.

Formula:

Mean = (Sum of all scores) ÷ (Number of scores)

5+4+1 =10

10/3

What is homoscedasticity?

A: Equal spread of scores → required for parametric tests

Q: What is heteroscedasticity

Unequal variance; fan-shaped scatterplot.

Q: What happens if data violates assumptions?

Use nonparametric tests.

nominal = categories only no order no numbers with meaning - labeling things gender eye color - how many are in each group you cant say one is more you can only say how many comparing frequencies

ordinal= ranking thinkg class rank 1,2,3, mild, moderate, severe, you know that one is more but not by how much more pain level 2 vs 4 is not guranteed to be twice as much of pain - average is questionable

Parametric tests assume the data is

normally distributed

interval = no a true zero bc 0°F does not mean “no temperature.” it just means its zero outside which is still a temp. Interval = Imaginary zero

ratio = zero means none age weight height ex if your zero age that mean your nothing etc Ratio = Real zero

Compare 2 independent group means

Independent t-test (parametic)

Mann–Whitney U (non parametic)

Compare 2 related means (same group twice

Paired t-test (parametric)

Wilcoxon Signed-Rank (non parametic)

Compare 3+ independent group means

One-Way ANOVA (parametic)

Kruskal–Wallis (non parametic)

Compare 3+ related measures

Repeated Measures ANOVA (parametic)

Friedman Test (non parametric)

Measure relationship between 2 variables

Pearson r (parametic)

Spearman’s rho (non parametric)

Compare frequencies or categories

no parametric version

Chi-square (non parametic version)

Most Tested Pairings

• ANOVA → Kruskal–Wallis

• t-test → Mann–Whitney U

• Pearson r → Spearman rho

A counselor wants to compare self-esteem scores for clients in four different treatment programs. Scores are measured on a 1–5 rating scale, the distribution is skewed, and variance differs across groups.

Which test should be used?

A. One-way ANOVA
B. Independent t-test
C. Kruskal–Wallis
D. Pearson r

A researcher examines the relationship between class rank and stress level rankings. Both variables are ordinal.

Which statistical test is most appropriate?

A. Pearson r
B. Spearman’s rho
C. Chi-square
D. Paired t-test

A study measures anxiety in the same clients before and after treatment. Scores are not normally distributed.

Which test should be used?

A. Paired t-test
B. Wilcoxon Signed-Rank
C. Mann–Whitney U
D. Repeated Measures ANOVA

A counselor wants to see if gender (male/female) is related to diagnosis category (depression, anxiety, PTSD).

Which test is best?

A. Pearson r
B. Chi-square
C. ANOVA
D. Mann–Whitney U

A researcher compares depression scores of two unrelated therapy groups. Data is normally distributed and measured on an interval scale.

Which test is appropriate?

A. Mann–Whitney U
B. Independent t-test
C. Wilcoxon Signed-Rank
D. Kruskal–Wallis

A study compares test scores for three teaching methods. Data is normally distributed.

Which test should be used first?

A. Post-hoc test
B. Independent t-test
C. One-way ANOVA
D. Chi-square

A counselor studies whether hours of sleep predicts anxiety score. Data is continuous and normally distributed.

Which test is best?

A. Pearson r
B. Spearman rho
C. Chi-square
D. Kruskal–Wallis

A researcher measures depression levels in clients at three time points (pre, mid, post). Data is skewed.

Which test is best?

A. Repeated Measures ANOVA
B. Friedman Test
C. Kruskal–Wallis
D. Paired t-test

A study examines the relationship between favorite coping style (problem-focused, emotion-focused, avoidant) and recovery status (improved/not improved).

Which test?

A. ANOVA
B. Pearson r
C. Chi-square
D. Spearman rho

A counselor compares impulsivity scores between two matched partners in couples therapy. Scores are not normally distributed.

Which test?

A. Independent t-test
B. Wilcoxon Signed-Rank
C. Mann–Whitney U
D. Kruskal–Wallis