Statistics Flashcards
Descriptive Statistics
Used to describe and summarize data.
Inferential Statistics
Techniques for making inferences about unknowns.
Range
Difference between largest and smallest values.
Standard Deviation
Measures spread of data around the mean.
±2 Standard Deviations
Covers approximately 95% of data in normal distribution.
±1.96 Standard Errors
Used for calculating 95% confidence intervals.
Chi-squared Test
Statistical test for categorical data analysis.
Spearman’s Rank Correlation Coefficient
Measures strength and direction of association.
Student’s t-test
Compares means between two groups.
Mean
Average value of a data set.
Mode
Most frequently occurring value in data.
Median
Middle value when data is ordered.
Outliers
Data points significantly different from others.
Distribution
Shape of data representation on a graph.
Thin Curve
Indicates values are close to the average.
Fat Curve
Indicates wider spread of values around mean.
Statistical Test Selection
Choosing appropriate test based on data type.
Electronic Calculators
Tools for calculating statistical test results.
Worked Examples
Illustrations of statistical concepts in practice.
Confidence Interval
Range of values likely to contain population parameter.
Statistical Significance
Indicates likelihood results are not due to chance.
Data Variability
Extent to which data points differ from each other.
Judgements in Statistics
Making conclusions based on statistical analysis.
Graphical Representation
Visual display of data trends and patterns.
Classwork Expectations
Understanding and applying statistical concepts in practice.
Written Examinations
Assess understanding without performing calculations.
Statistical Interpretation
Explaining results of statistical tests.
Mixed Questions
Final assessments covering various statistical topics.
Standard Deviation
Measure of data dispersion from the mean.
Formula for SD
SD = √Σ(x - x̄)² / (n - 1)
X
Individual data value in the dataset.
x̄ (mean)
Average of all data values.
n
Total number of data values.
Normal Distribution
Data follows a bell-shaped curve.
± 2 Standard Deviations
Covers 95% of data in normal distribution.
Bristol Zoo Mean Age
Mean age of lions is 32.3 months.
London Zoo Mean Age
Mean age of lions is 48.8 months.
Bristol Zoo SD
Standard deviation of lions is 9.3 months.
London Zoo SD
Standard deviation of lions is 1.7 months.
2 x SD (Bristol)
18.6 months; range from mean.
2 x SD (London)
2.4 months; range from mean.
Mean + (2 x SD) Bristol
50.9 months; upper limit for comparison.
Mean - (2 x SD) Bristol
13.7 months; lower limit for comparison.
Mean + (2 x SD) London
51.2 months; upper limit for comparison.
Mean - (2 x SD) London
46.4 months; lower limit for comparison.
Overlap of SD Bars
Indicates chance differences in means.
Fish Length Female Mean
Mean length is 21 cm.
Fish Length Male Mean
Mean length is 10 cm.
Fish Female SD
Standard deviation is 3 cm.
Fish Male SD
Standard deviation is 1.6 cm.
Mean + (2 x SD) Fish Female
27 cm; upper limit for comparison.
Mean - (2 x SD) Fish Female
15 cm; lower limit for comparison.
Mean + (2 x SD) Fish Male
13 cm; upper limit for comparison.
Mean - (2 x SD) Fish Male
7 cm; lower limit for comparison.
Heart Rate Data
Comparison of heart rates during TV shows.
Standard Error of the Mean
Estimates the accuracy of sample mean.
95% Confidence Interval
Range where true population mean likely lies.
Mean
Average value of a sample data set.
Standard Error (SE)
Estimate of the variability of sample means.
Standard Deviation (SD)
Measure of data dispersion in a sample.
95% Confidence Interval (CI)
Range where true mean likely falls, 95% certainty.
Upper Confidence Limit
Maximum value in the confidence interval.
Lower Confidence Limit
Minimum value in the confidence interval.
Sample Size (n)
Number of observations in a sample.
1.96
Z-score for 95% confidence level.
Confidence Level
Probability that the CI contains the true mean.
Overlap of Intervals
Indicates similarity between two sample means.
Graphical Representation
Visual display of confidence intervals.
Estimate of the Mean
Sample mean used to infer population mean.
Random Sampling
Selecting samples randomly from a population.
Worked Example
Illustrative calculation using sample data.
Guinea Pig Mass
Sample data used for mean calculation.
Limpet Size Comparison
Study comparing sizes between two ledges.
Data Collection
Process of gathering information for analysis.
Statistical Significance
Likelihood that a result is not due to chance.
Population Mean
Average value of a complete population.
Calculation of CI
Using mean and SE to find confidence limits.
Non-overlapping Intervals
Indicates significant difference between two means.
Mean + 1.96 x SE
Upper limit calculation for confidence interval.
Mean - 1.96 x SE
Lower limit calculation for confidence interval.
Sample Data
Subset of population used for statistical analysis.
Estimation
Approximation of a population parameter based on sample.
Statistical Analysis
Method of interpreting data to draw conclusions.
Callipers Measurement
Tool used for measuring sizes in the example.
Data Presentation
Organizing data for clear interpretation.
Standard Error (SE)
Measure of variability of sample mean estimates.
Confidence Interval (CI)
Range estimating population parameter with specified confidence.
Standard Deviation (SD)
Measure of data dispersion around the mean.
95% Confidence Interval
Range where true mean lies with 95% certainty.
Overlap in CI
Indicates potential similarity between two means.
BMI (Body Mass Index)
Measure of body fat based on height and weight.
South Beach Diet
Diet focused on reducing carbohydrate intake.
Low Calorie Diet
Diet aimed at reducing overall calorie consumption.
Reduction in BMI
Decrease in body mass index percentage.
Quadrat Sampling
Method for estimating population density in ecology.
Runner Bean
Type of climbing plant grown for its edible pods.
Height Measurement
Assessment of plant growth in centimeters.
Random Sampling
Selection method ensuring each member has equal chance.
Null Hypothesis
Assumption that there is no effect or difference.
Alternative Hypothesis
Assumption that there is an effect or difference.
Fertilizer Types
Different substances used to enhance plant growth.
Data Interpretation
Analyzing results to draw conclusions from data.
Percent Reduction
Percentage decrease from an initial value.
Mean Height
Average height of plants in a sample.
Sample Mean Calculation
Sum of values divided by number of observations.
Statistical Analysis
Process of collecting and interpreting data.
Ecological Study
Research focused on interactions within ecosystems.
Experimental Design
Plan for conducting an experiment to test hypotheses.
Plant Growth Factors
Variables influencing the development of plants.
Comparative Analysis
Evaluating differences between two or more groups.
Chemical control
Method using chemicals to reduce pest populations.
Biological control
Using natural predators to manage pest species.
Standard error
Estimation of the variability of sample means.
95% confidence interval
Range where the true population parameter lies.
Mean number of plants
Average count of plants per square meter.
Field A
Field previously used for grazing cattle.
Field B
Field used for the same crop previously.
Mass of crop
Weight of crop measured in kg per m².
Mayfly nymphs
Aquatic larvae of mayflies found in streams.
Shallow water
Water with less depth, typically faster flow.
Deep water
Water with greater depth, typically slower flow.
Aorta thickness
Measurement of arterial wall thickness in micrometers.
Vena cava thickness
Measurement of venous wall thickness in micrometers.
Diastolic blood pressure
Pressure in arteries during heart relaxation.
Farm workers
Individuals working in agricultural settings.
Firemen
Individuals trained to combat fires.
Null hypothesis
Statement asserting no effect or difference exists.
Inferential statistics
Methods to draw conclusions from sample data.
Chickens hypothesis
Statement about male offspring production in chickens.
Slug population hypothesis
Statement regarding slug counts in different areas.
Tobacco growth hypothesis
Statement about growth rates in different soils.
Chi-squared test
Statistical test for categorical frequency comparison.
Frequencies
Counts of occurrences in different categories.
Significant difference
Statistical term indicating a meaningful variation.
Worked Example 1
Example illustrating chi-squared test application.
Periwinkle blush
Humorous reference to snails and seaweed.
Sample collection
Process of gathering data from selected subjects.
Statistical test
Procedure to evaluate hypotheses using data.
Crop mass comparison
Analysis of crop weight differences between fields.
Flat Periwinkle
A small snail living on seaweed.
Observed Frequency
Actual count of periwinkle on seaweed.
Serrated Wrack
Type of seaweed with 45 observed periwinkles.
Bladder Wrack
Type of seaweed with 38 observed periwinkles.
Egg Wrack
Type of seaweed with 10 observed periwinkles.
Spiral Wrack
Type of seaweed with 5 observed periwinkles.
Other Seaweed
Type of seaweed with 2 observed periwinkles.
Total Observed
Sum of all observed frequencies, 100.
Null Hypothesis
No significant difference in observed frequencies.
Expected Frequency
Average expected count per seaweed type.
Calculation of Expected Frequency
Total observed divided by number of categories.
Degrees of Freedom
Number of categories minus one.
Critical Value
Threshold for accepting or rejecting null hypothesis.
Chi-Squared Value
Indicates difference between observed and expected data.
Significance Level
Probability threshold for hypothesis testing.
p=0.05
Common significance level used in tests.
Chi-Squared Formula
Sum of (O-E)²/E for each category.
Calculated Chi-Squared
Total of Chi-squared calculations, 79.
Critical Value at p=0.05
9.49 for 4 degrees of freedom.
Rejecting Null Hypothesis
Indicates preference for certain seaweed.
Accepting Null Hypothesis
Indicates no preference for seaweed.
Observed vs Expected
Comparison of actual counts to predicted counts.
Chi-Squared Test
Statistical method for categorical data analysis.
Statistical Significance
Likelihood that results are not due to chance.
Hypothesis Testing
Method for making inferences about populations.
Data Sheet
Reference for critical values in tests.
Animal Preference
Tendency of periwinkles towards specific seaweed.
Statistical Analysis
Process of interpreting data using statistical methods.
Biological Study
Research focused on living organisms and their interactions.
Chi-squared
Statistical test for observed vs expected frequencies.
Null Hypothesis
Assumes no significant difference exists in data.
Observed Frequency
Actual count of occurrences in an experiment.
Expected Frequency
Theoretical count based on the null hypothesis.
Degrees of Freedom
Number of categories minus one in analysis.
Critical Value
Threshold for determining statistical significance.
Significance Level
Probability threshold for rejecting the null hypothesis.
P-value
Probability of observing data if null hypothesis is true.
Chi-squared Value
Calculated statistic comparing observed and expected frequencies.
Accept Null Hypothesis
Conclude no significant difference exists in data.
Reject Null Hypothesis
Conclude significant difference exists in data.
Biological Interpretation
Understanding biological implications of statistical results.
Chi-squared Test
Method to assess goodness of fit for categorical data.
Observed vs Expected
Comparison of actual data to theoretical predictions.
Mendel’s Peas
Study of inheritance patterns in pea plants.
Heterozygous Plants
Plants with two different alleles for a trait.
3:1 Ratio
Expected ratio of dominant to recessive traits.
Bird-Table Experiment
Study of bird visitation across different gardens.
Garden Observations
Counts of birds visiting three different gardens.
Chi-squared Calculation
Formula: Σ((O-E)²/E) for data analysis.
Biologist’s Inference
Conclusion drawn from statistical analysis of species.
Statistical Critique
Evaluation of methodology and assumptions in analysis.
Probability Threshold
Cutoff for determining significance, often 5%.
Random Distribution
Even spread of occurrences without bias.
Bird Visitation Hypothesis
Assumption about bird preferences for garden locations.
Aggression in Primates
Behavioral study related to environmental conditions.
Light Intensity Impact
Effect of lighting on animal behavior.
Chi-squared Worked Example
Illustrative case demonstrating chi-squared application.
Incidences of Aggression
Count of aggressive behaviors observed in a study.
Null Hypothesis
Assumes no effect or difference exists in data.
Chi-squared Value
Statistical measure to compare observed vs expected frequencies.
Degrees of Freedom
Number of independent values in a statistical calculation.
Critical Value
Threshold for determining statistical significance in tests.
Observed Frequencies
Actual counts recorded in an experiment or study.
Expected Frequencies
Predicted counts based on the null hypothesis.
Bee-eaters
Birds that primarily feed on bees and wasps.
Forest Floor
Ground layer of a forest ecosystem.
Understory Layer
Layer beneath the forest canopy, rich in vegetation.
Canopy Layer
Upper layer of a forest formed by tree crowns.
Emergent Layer
Top layer of a forest where tallest trees grow.
Grassland Field
Open area dominated by grasses and few trees.
River-bank
Land alongside a river, often rich in biodiversity.
Fish Species
Different types of fish counted in a study.
Colour Blindness
Inability to distinguish certain colors, more common in males.
Urgent Appointment Requests
Number of patients seeking immediate medical attention.
DNA Hybridisation
Technique to measure genetic similarity between species.
Tuberculosis Cases
Reported instances of TB in a specific population.
Mean Percentage DNA Hybridisation
Average genetic similarity percentage between crane species.
Statistically Significant Differences
Differences that are unlikely to occur by chance.
Spearman’s Rank Correlation
Test assessing association between two ranked variables.
Aggression Observations
Data collected regarding aggressive behavior occurrences.
Statistical Test
Method to analyze data and draw conclusions.
Sample Size
Number of observations or data points in a study.
Frequency Distribution
Summary of how often each value occurs.
Hypothesis Testing
Procedure to determine if a hypothesis is supported.
Positive correlation
Variables increase together, showing a direct relationship.
Negative correlation
One variable increases while the other decreases.
No correlation
No discernible relationship between two variables.
Line of best fit
A straight line that best represents data points.
Spearman’s rank correlation coefficient (rs)
Statistical measure of rank correlation between variables.
Null hypothesis
Assumes no relationship exists between two variables.
Critical value
Threshold to accept or reject the null hypothesis.
D2
Squared differences in ranks for paired measurements.
Rank the data
Assign ranks from lowest to highest values.
Tied scores
Scores that share ranks receive average rank.
Statistically significant
Results unlikely due to chance, indicating a relationship.
Paired measurements
Two related data points for comparison.
Correlation significance test
Determines if correlation is statistically meaningful.
Uphill line
Graph representation indicating positive correlation.
Length (metres)
Measurement of blue whale’s length in meters.
Mass (tonnes)
Measurement of blue whale’s mass in tonnes.
Sum of D2 (∑D2)
Total of squared differences in ranks.
Equation for rs
Formula used to calculate Spearman’s rank correlation.
Value of rs
Indicates strength and direction of correlation.
Perfect positive correlation
Correlation value of 1 indicates complete agreement.
Perfect negative correlation
Correlation value of -1 indicates complete opposition.
Significance level
Probability threshold for determining statistical significance.
Rank of variable 1
Ranking assigned to the first variable’s data.
Rank of variable 2
Ranking assigned to the second variable’s data.
Mean rank
Average rank assigned to tied scores.
Correlation coefficient interpretation
Understanding the meaning of the correlation value.
Rejecting the null hypothesis
Concluding a relationship exists between variables.
Positive correlation
Relationship where both variables increase together.
Negative correlation
Relationship where one variable increases, the other decreases.
Null hypothesis
Assumes no correlation between studied variables.
Spearman’s rank correlation coefficient
Statistical measure of correlation using ranks.
Critical value
Threshold to determine significance of correlation.
Quadrat
Frame used to sample plants in ecology.
Moorland restoration
Rehabilitating moorland ecosystems for biodiversity.
Paired readings
Data points collected in matched sets.
Rank data
Ordering data points from smallest to largest.
D (Difference)
Difference between ranks of two variables.
D² (Squared difference)
Square of the difference D.
∑D²
Sum of all squared differences.
n (sample size)
Total number of paired observations.
Volume (cm³)
Space occupied by the bird’s throat pouch.
Frequency (Hz)
Number of sound waves produced per second.
Drumming sound
Mating call produced by male Frigatebirds.
Ecologist
Scientist studying ecosystems and environmental interactions.
Plant species correlation
Relationship between growth of different plant types.
Restored moorland
Moorland that has been rehabilitated post-disturbance.
Statistical significance
Likelihood that result is not due to chance.
Correlation analysis
Statistical method to assess relationships between variables.
Hypothesis testing
Method to determine validity of a hypothesis.
Plant density
Number of plants per unit area.
Frigatebird
Bird species known for its distinctive pouch.
Ecological monitoring
Regular observation to assess environmental changes.
Correlation coefficient interpretation
Evaluating strength and direction of a relationship.
Restoration year
Year when the moorland was rehabilitated (2003).
Pouch size
Measurement of the Frigatebird’s throat pouch.
Volume estimation
Calculating the size of the pouch in cm³.
Spearman’s rank correlation coefficient
Statistical measure of correlation between two variables.
Critical value
Threshold value to determine significance of correlation.
Null hypothesis
Assumption that there is no effect or relationship.
Probability of chance
Likelihood that results occurred randomly.
Purple loosestrife
Invasive plant species targeted for biological control.
Biological control
Using natural predators to manage pest populations.
Mean number of beetles
Average count of beetles per square meter.
Rank the data
Ordering data points from lowest to highest.
Calculate Spearman’s rank
Compute correlation based on ranked data.
Difference (D)
Discrepancy between ranks of two variables.
D squared (D²)
Square of the difference values.
Sum of D squared (∑D²)
Total of all squared differences.
Sample size (n)
Total number of observations in the study.
Blood sugar concentration
Amount of glucose in blood, measured in mg.
Time of day
Specific hour when blood glucose was measured.
Mean number of plant species
Average count of species on roundabouts.
Mowing frequency
Interval at which grass is cut on roundabouts.
Biodiversity
Variety of plant and animal species in an area.
Significant relationship
Statistically meaningful connection between two variables.
Carbohydrates
Nutrients that increase blood glucose levels.
Glucose concentration
Measurement of sugar level in blood.
Interval between mowing
Time period between grass cutting sessions.
Investigative study
Research conducted to explore a specific hypothesis.
Ecologists
Scientists who study ecosystems and biodiversity.
Road junctions
Intersections where roads meet, often with roundabouts.
Statistical significance
Probability that results are not due to chance.
Correlation
Relationship between two variables, indicating association.
Mean number of plant species
Average count of different plant species observed.
Null hypothesis
Assumes no significant difference exists between groups.
Spearman’s rank correlation coefficient
Non-parametric measure of rank correlation between variables.
∑D²
Sum of squared differences in ranks.
rs value
Spearman’s rank correlation coefficient value calculated.
Critical value
Threshold for determining significance in correlation.
5% probability
Threshold for statistical significance in hypothesis testing.
Temperature (°C)
Independent variable affecting rate of respiration.
Rate of respiration
Measured by bubbles produced per minute.
Egg mass (g)
Weight of eggs in grams.
Chick mass (g)
Weight of chicks at hatching in grams.
Shell length (mm)
Length of mussel shells measured in millimeters.
Shell width (mm)
Width of mussel shells measured in millimeters.
Mood correlation
Relationship between mood and liquid consumption.
Liquid consumed
Amount of liquid intake measured daily.
Body height correlation
Relationship between height and biological age.
Growth rate of bacteria
Rate at which bacteria multiply in culture.
Citric acid concentration
Amount of citric acid in growth medium.
Student’s t-test
Statistical test comparing means of two groups.
Significant difference
Statistically meaningful variation between two means.
Replicate flasks
Multiple samples used for reliable measurement.
Mean value
Average calculated from a set of measurements.
Bacterium A
First strain of bacteria in the experiment.
Bacterium B
Second strain of bacteria in the experiment.
Flask measurements
Data collected from individual bacterial cultures.
Worked example
Illustrative calculation demonstrating statistical methods.
Correlation interpretation
Analysis of relationship strength between two variables.
Negative correlation
Inverse relationship where one variable increases, the other decreases.
Positive correlation
Direct relationship where both variables increase together.
Equilibrate temperature
Allowing yeast temperature to stabilize with water bath.
Bacterium A
First type of bacteria studied in the experiment.
Bacterium B
Second type of bacteria compared in the experiment.
Mean
Average value calculated from data set.
Standard Deviation (s)
Measure of data variability around the mean.
Variance (s²)
Square of the standard deviation, indicates data spread.
s² ÷ n
Variance divided by sample size, used in t-test.
t-value
Calculated statistic used to compare means.
Degrees of Freedom
Number of independent values in a calculation.
Critical Value
Threshold for determining significance in hypothesis testing.
Null Hypothesis
Assumption stating no significant difference exists.
t-test
Statistical test comparing means of two groups.
Significant Difference
Statistical indication that results are unlikely due to chance.
Acid Gastric Juices
Stomach secretions that kill most bacteria.
Urease
Enzyme that neutralizes gastric acid by producing ammonia.
Ammonia
Base produced by urease, neutralizes stomach acid.
Temperature Effect
Impact of temperature on enzyme activity.
Sample Size (n)
Number of observations in each group.
Interpreting Results
Analyzing calculated t-value against critical value.
Mean Mass
Average weight of bacteria measured in the study.
Probability Threshold
Standard cutoff (5%) for significance in tests.
Data Sheet
Reference table for critical values based on degrees of freedom.
Statistical Significance
Likelihood that results are not due to random chance.
Comparison of Means
Evaluating differences between average values of two groups.
Flask Experiment
Experimental setup using flasks to grow bacteria.
Temperature Readings
Measurements taken at different temperatures for analysis.
Results Table
Organized data showing outcomes of the experiment.
Haemoglobin reading
Measurement of hemoglobin concentration in g/dL.
Mean
Average value calculated from a data set.
Standard deviation (s)
Measure of data dispersion around the mean.
Variance (s²)
Square of the standard deviation, indicating spread.
t-value
Calculated statistic for comparing group means.
Cell cycle time
Duration for one complete cycle of cell division.
Mitosis rate
Speed of cell division in a given time.
Chi-squared test
Statistical test for association between categorical variables.
Correlation coefficient
Measure of strength and direction of relationship.
Allele frequency
Proportion of a specific allele in a population.
Probability
Likelihood of occurrence of an event.
Random sampling
Selecting individuals from a population randomly.
Bacterium A and B
Two groups compared for mean mass differences.
Significant difference
Statistically meaningful variation between two groups.
Flowchart for tests
Guide for selecting appropriate statistical tests.
Fur seals
Marine mammals breeding in Antarctic regions.
Frequency of b allele
Rate of occurrence of the recessive allele.
Statistical test justification
Rationale for choosing a specific statistical method.
Comparing frequencies
Analyzing counts of occurrences in different groups.
Bacterial mass comparison
Analysis of weight differences between two bacteria.
Results interpretation
Understanding outcomes based on statistical analysis.
Cell division comparison
Evaluating mitosis rates in different cell types.
Significant increase
Notable rise in data over a period.
Statistical analysis
Process of collecting and interpreting quantitative data.
Null Hypothesis
Assumption stating no effect or difference exists.
Probability
Likelihood of an event occurring, expressed as a fraction.
Chance
Random occurrence of events without predictability.
Return Rate
Rate of food delivery to nest per time.
Statistical Test
Method to determine significance of results.
Significantly Better Provider
Provider with higher return rate for chicks.
Malaria
Disease caused by a parasite affecting lizards.
Anolis Lizard
Genus of lizards studied for malaria effects.
Elevation
Height above sea level, affecting lizard infection rates.
Percentage Infected
Proportion of lizards infected with malaria.
Light Intensity
Amount of light measured in Lux affecting photosynthesis.
Photosynthesis Rate
Number of bubbles produced per minute by Elodea.
Statistical Significance
Probability results are not due to chance.
Dihybrid Cross
Genetic cross examining two traits simultaneously.
Expected Ratio
Theoretical proportion of phenotypes in offspring.
Observed Results
Actual counts of phenotypes from the experiment.
Moss Growth Comparison
Analysis of moss area on tree sides.
Seedling Growth Measurement
Length increase of seedlings under different light.
Mean Increase
Average growth measurement across multiple trials.
Return Rate Calculation
Measured in mg/hour for feeding efficiency.
Infection Sampling
Collecting data on lizard populations over time.
Statistical Justification
Reasoning for choosing a specific statistical test.
Correlation Test
Determines relationship between two variables.
T-Test
Compares means between two groups for significance.
Chi-Squared Test
Assesses differences between observed and expected frequencies.
Light Reflection Intensity
Measured light reflected by colored segments.
Experimental Repetition
Conducting trials multiple times for reliability.
Data Collection Interval
Time period between data sampling events.
Breeding Behavior
Parental actions in providing for offspring.
Statistical Analysis
Process of interpreting data to draw conclusions.
Experimental Control
Conditions kept constant to ensure valid results.
Sample Size
Number of subjects included in the study.
Data Interpretation
Analyzing results to understand biological implications.
