Data Handling and analysis

Question 1

Levels of Measurement

Answer 1

1. Nominal Data
   o Definition: Data in categories (e.g., gender, blood type).
   o Strength: Easy to generate from closed questions.
   o Limitation: Lacks depth; cannot express relative magnitude.
2. Ordinal Data
   o Definition: Data that can be ordered, but intervals between values are not equal (e.g., ranks, rating scales).
   o Strength: Provides some order of magnitude.
   o Limitation: Differences between scores are subjective.
3. Interval Data
   o Definition: Data with equal intervals between values but no true zero (e.g., temperature in Celsius).
   o Strength: Precise, allows for more detailed analysis.
   o Limitation: Cannot establish a true absence of the variable.
4. Ratio Data
   o Definition: Data with equal intervals and a true zero point (e.g., height, weight).
   o Strength: Allows for the comparison of magnitudes.
   o Limitation: Not as common in psychological research.

Question 2

Descriptive Statistics

Answer 2

1. Mean
   o Definition: Sum of all values divided by the number of values.
   o Strength: Uses all data points, providing a precise measure.
   o Limitation: Affected by extreme scores (outliers).
2. Median
   o Definition: Middle value when data is arranged in order.
   o Strength: Unaffected by outliers.
   o Limitation: Doesn’t consider the magnitude of all values.
3. Mode
   o Definition: Most frequently occurring value.
   o Strength: Useful for categorical data.
   o Limitation: Can be uninformative if multiple modes or no mode exist.

Question 3

Measures of Dispersion

Answer 3

1. Range
   o Definition: Difference between the highest and lowest scores.
   o Strength: Simple and quick to calculate.
   o Limitation: Affected by outliers, doesn’t represent the distribution.
2. Standard Deviation (SD)
   o Definition: A measure of the average distance from the mean.
   o Strength: Provides a more precise measure of variability.
   Limitation: Can be complex to calculate and interpret for non-experts.

Question 4

Types of Distributions

Answer 4

1. Normal Distribution
   o Definition: A symmetrical, bell-shaped curve where most scores cluster around the mean.
   o Features: Mean = Median = Mode, and 68% of scores fall within 1 SD of the mean.
2. Skewed Distribution
   o Positive Skew: Tail extends to the right (mean > median > mode).
   o Negative Skew: Tail extends to the left (mean < median < mode).
3. Kurtosis
   o Leptokurtic: Sharp peak (high kurtosis).
   Platykurtic: Flat distribution (low kurtosis).

Question 5

Inferential Statistics

Answer 5

1. Parametric Tests
   o Assumptions: Normally distributed data, interval/ratio level, equal variances.
   o Examples: t-test, ANOVA.
2. Non-Parametric Tests
   o Used when data doesn’t meet parametric assumptions.
   o Examples: Mann-Whitney U, Wilcoxon, Chi-Square.
3. Choosing Tests
   o Correlation: Pearson’s r (parametric), Spearman’s rho (non-parametric).
   o Difference between Groups: t-test (parametric), Mann-Whitney U (non-parametric).

Question 6

Significance and Probability

Answer 6

1. p-value
   o The probability of obtaining a result if the null hypothesis is true.
   o Significance Level: Typically set at 0.05 (5%). If p < 0.05, results are statistically significant.
2. Type I Error
   o Rejecting the null hypothesis when it’s true (false positive).
3. Type II Error
   o Failing to reject the null hypothesis when it’s false (false negative).

Question 7

Effect Size

Answer 7

1. Definition: A measure of the strength or magnitude of the effect or relationship found in a study.
2. Cohen’s d
   o Measures the difference between two means.
   o Small Effect: 0.2
   o Medium Effect: 0.5
   o Large Effect: 0.8 or above.
3. Importance: Even if a result is statistically significant, the effect size tells us how practically significant it is.

Question 8

Correlations

Answer 8

1. Positive Correlation
   o As one variable increases, so does the other.
2. Negative Correlation
   o As one variable increases, the other decreases.
3. No Correlation
   o No relationship between variables.
4. Correlation Coefficient
   o A statistical value (ranging from -1 to +1) that indicates the strength and direction of a relationship.

Question 9

Presentation of Data

Answer 9

1. Bar Chart
   o Used for discrete data, where categories are separate (e.g., gender).
2. Histogram
   o Used for continuous data, where bars touch to show the distribution of scores.
3. Scatterplot
   o Shows the relationship between two continuous variables (used in correlation studies).
4. Tables
   o Used to present raw data and descriptive statistics clearly.

Question 10

Significance Testing and Statistical Tests

Answer 10

1. Chi-Square Test
   o Used for nominal data to assess differences between groups or associations between variables.
2. Mann-Whitney U Test
   o A non-parametric test for comparing differences between two independent groups (ordinal data).
3. Wilcoxon Signed-Rank Test
   o A non-parametric test for comparing differences between two related groups.