All questions

Statistics Basics

E numbers

Question 1

Which is bigger?

viewof scientific_notation_1_response = Inputs.radio(['3.1e3','310']);
correct_scientific_notation_1 = '3.1e';
scientific_notation_1_result = {
  if(scientific_notation_1_response == correct_scientific_notation_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Which is bigger?

viewof scientific_notation_2_response = Inputs.radio(['2.5 * 10^-3',' .00025']);
correct_scientific_notation_2 = '2.5 * 10^-3';
scientific_notation_2_result = {
  if(scientific_notation_2_response == correct_scientific_notation_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

General

Question 1

Assuming that you are investigating a real effect, which sample size is more likely to give you a significant result?

viewof stats_basics_1_response = Inputs.radio(['100','200','neither']);
correct_stats_basics_1 = '100';
stats_basics_1_result = {
  if(stats_basics_1_response == correct_stats_basics_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Assuming that you are NOT investigating a real effect, which sample size is more likely to give you a significant result?

viewof stats_basics_2_response = Inputs.radio(['100','200','neither']);
correct_stats_basics_2 = 'neither';
stats_basics_2_result = {
  if(stats_basics_2_response == correct_stats_basics_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 3

Alpha values are…

viewof stats_basics_3_response = Inputs.radio(['higher when the p-value is higher','lower when the p-value is lower','neither']);
correct_stats_basics_3 = 'neither';
stats_basics_3_result = {
  if(stats_basics_3_response == correct_stats_basics_3){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Probability

Question 1

What is the likelihood of flipping a (non-biased) coin heads and then tails?

viewof probability_1_response = Inputs.number();
correct_probability_1 = .025;
probability_1_result = {
  if(probability_1_response == correct_probability_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

What is the likelihood of rolling 3 sixes in a row?

viewof probability_2_response = Inputs.radio(['(1/6)*3','(1/6)^3','(1/6)+3']);
correct_probability_2 = '(1/6)^3';
probability_2_result = {
  if(probability_2_response == correct_probability_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Describing Data

Central Tendency

Question 1

Which of the following is most influenced by outliers?

viewof central_tendency_1_response = Inputs.radio(['Mean','Median']);
correct_central_tendency_1 = 'Mean';
central_tendency_1_result = {
  if(central_tendency_1_response == correct_central_tendency_1){
    return 'Correct! Median is unlikely to be influenced by a single value, whereas an extreme value can drag the mean up or down.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Dispersion

Question 1

True or False: Using degrees of freedom (N-1) rather than N controls for bias

viewof dispersion_1_response = Inputs.radio(['True','False']);
correct_dispersion_1 = 'True';
dispersion_1_result = {
  if(dispersion_1_response == correct_dispersion_1){
    return 'Correct! Note that bias does not apply to means, but applies to estimates of distribution like variance and SD.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Which of the following can be negative?

viewof dispersion_2_response = Inputs.radio(['SD','Variance','Both']);
correct_dispersion_2 = 'SD';
dispersion_2_result = {
  if(dispersion_2_response == correct_dispersion_2){
    return 'Correct! Variance cannot be negative because it is SD^2, and squared values are always positive.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Distributions

Binomial

Question 1

Do binomial distributions only work if there is an equal likelihood of either outcome?

viewof binomial_1_response = Inputs.radio(['Yes','No']);
correct_binomial_1 = 'No';
binomial_1_result = {
  if(binomial_1_response == correct_binomial_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

What is the likelihood of flipping 2 heads in a row if your coin is .6 biased towards heads

viewof binomial_2_response = Inputs.number();
correct_binomial_2 = '.36';
binomial_2_result = {
  if(binomial_2_response == correct_binomial_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Normal

Question 1

rand_maths_score = 40 + Math.round(Math.random() * 60);
mean_maths_score = 70
sd_maths_score   = 10

Jamie has just completed a mathematics test, where the maximum score is 100%. Their score was , the mean maths score was and the SD was . What is their Z-score?

viewof normal_question_1_response = Inputs.number([-7,3], {label: "Z-score", step:.1});
correct_z_score = (rand_maths_score - mean_maths_score)/sd_maths_score;

normal_question_1_result = { 
  if(normal_question_1_response == correct_z_score){
    return "Correct! (" + rand_maths_score + " - " + mean_maths_score + ")/" + sd_maths_score + " = " + correct_z_score;
  } else {
    return "Missing or incorrect. Remember that how Z is calculated by dividing the difference between a value and the mean value by the SD."
  } 
}

Your answer is… .

Question 2

Using the above value, which percentile group would you put Jamie’s score into?

normal_question_2_correct = {
  if(correct_z_score < -2){
    return "bottom 2.3%";
  } else if(correct_z_score < -1){
    return "bottom 15.9%";
  } else if(correct_z_score < 0){
    return "bottom 50%";
  } else if(correct_z_score < 1){
    return "top 50%";
  } else if(correct_z_score < 2){
    return "top 15.9%";
  } else {
    return "top 2.3%";
  }
}

viewof normal_question_2_response = Inputs.radio([
  "bottom 2.3%", 
  "bottom 15.9%",
  "bottom 50%",
  "top 50%",
  "top 15.9%",
  "top 2.3%", 
  ], {label: "", value: "A"});
normal_question_2_result = { 
  if(normal_question_2_response == ""){
    return "awaiting your response";
  } else if(normal_question_2_correct == normal_question_2_response){
    return "Correct!";
  } else {
    return "Missing or Incorrect - have a look at the plots above to help you find the correct answer. Note, the distributions are symmetrical, so the pattern for the top half will mirror that for the bottom half.";
  }
}

Your answer is… .

If you want to practice with different numbers in these questions then please reload the page.

Skewness

Question 1

rand_skew_no = Math.round(Math.random() * 400)/100;

Is a skewness z-score of indicative of a significant problem of skewness?

viewof skewness_question_1_response = Inputs.radio(["Yes", "No"], {label: "", value: "A"});
this_result = { 
  var skewness_question_1_result = "awaiting response";

  if(rand_skew_no > 1.96){
    if(skewness_question_1_response == "Yes"){
      skewness_question_1_result = "Correct - Z scores above 1.96 suggest significant problems with skewness";
    } else if(skewness_question_1_response == "No") {
      skewness_question_1_result = "Not Correct - Z scores above 1.96 suggest significant problems with skewness";
    }
  } else {
    if(skewness_question_1_response == "Yes"){
      skewness_question_1_result = "Not Correct - Z scores below 1.96 **do not** suggest significant problems with skewness";
    } else if(skewness_question_1_response == "No") {
      skewness_question_1_result = "Correct  - Z scores below 1.96 **do not** suggest significant problems with skewness";
    }
  }
  return skewness_question_1_result;
}

Your answer is

Transforming Data

Question 1

Which types of transformations might make a distribution normal?

viewof transformation_1_response = Inputs.radio(['linear','non-linear']);
correct_transformation_1 = 'non-linear';
transformation_1_result = {
  if(transformation_1_response == correct_transformation_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete. The pattern of a distribution does not change after linear transformations.';
  };
}

Question 2

Which of the following transformations is least likely to result in a normal distribution?

viewof transformation_2_response = Inputs.radio(['log','square','square-root']);
correct_transformation_2 = 'square';
transformation_2_result = {
  if(transformation_2_response == correct_transformation_2){
    return 'Correct! Squaring your distribution will exagerate even relative differences between your data points, and thus likely to skew your distribution.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Correlations

Correlations

Question 1

Which test would be less influenced by skewed data?

viewof correlations_1_response = Inputs.radio(["Pearson's R","Spearman's Rho/Rank"]);
correct_correlations_1 = "Spearman's Rho/Rank";
correlations_1_result = {
  if(correlations_1_response == correct_correlations_1){
    return 'Correct! Ranks are less influenced by outliers which can skew the data than raw data.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Can r values be greater than 1?

viewof correlations_2_response = Inputs.radio(['Yes, if the association is super strong','No, never ever']);
correct_correlations_2 = 'No';
correlations_2_result = {
  if(correlations_2_response == correct_correlations_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Partial Correlations

Question 1

What does a variable need to correlate with to be a viable candidate as a covariate?

viewof partial_correlations_1_response = Inputs.radio(['Both other variables','At least one other variable','No other variables']);
correct_partial_correlations_1 = 'Both other variables';
partial_correlations_1_result = {
  if(partial_correlations_1_response == correct_partial_correlations_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Regressions

Simple Regressions

Question 1

Is an r-value a standardised or unstandardised estimate of the association between a predictor and an outcome?

viewof simple_regression_1_response = Inputs.radio(['Standardised','Unstandardised']);
correct_simple_regression_1 = 'Standardised';
simple_regression_1_result = {
  if(simple_regression_1_response == correct_simple_regression_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Multiple Regressions

Categorical

Contingency

Question 1

Will Cramer’s V give the same value as Phi?

viewof contingency_1_response = Inputs.radio(['Yes','No']);
correct_contingency_1 = 'Yes';
contingency_1_result = {
  if(contingency_1_response == correct_contingency_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Chi Square tests tell you…

viewof contingency_2_response = Inputs.radio(['Effect size','Significance']);
correct_contingency_2 = 'Significance';
contingency_2_result = {
  if(contingency_2_response == correct_contingency_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Item Analysis

Cronbach Alpha

Question 1

Cronbach’s Alpha is useful to check whether items in a measure are…

viewof cronbach_alpha_1_response = Inputs.radio(['valid','reliable']);
correct_cronbach_alpha_1 = 'reliable';
cronbach_alpha_1_result = {
  if(cronbach_alpha_1_response == correct_cronbach_alpha_1){
    return 'Correct! Specifically, whether they reliably measure the same construct. However, weird things can happen if multiple similar constructs are captured in the measure, so it can be helpful to conduct Principle Component Analysis first.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Do you need to reverse code relevant items before conducting Cronbach’s Alpha?

viewof cronbach_alpha_2_response = Inputs.radio(['Yes','No']);
correct_cronbach_alpha_2 = 'Yes';
cronbach_alpha_2_result = {
  if(cronbach_alpha_2_response == correct_cronbach_alpha_2){
    return 'Correct! Otherwise the item will reduce the alpha value even if the item is reliably associated with other items (just going in the opposite direction).';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Multiple testing

Family-Wise Error Rate

Question 1

An alpha value of .05 suggests that 5% of published studies are false-positives?

viewof fwer1_response = Inputs.radio(['True','False']);
correct_fwer1 = 'False';
fwer_1color = {
  if(fwer1_response == correct_fwer1){
    return 'blue';
  } else {
    return 'red';
  }   
}
fwer1_result = {
  if(fwer1_response == correct_fwer1){
    return 'Correct! It suggests that 5% of studies that investigate effects that do not exist in the population will find them in the sample. However, if no studies are investigating effects that are real in the population then 100% of published studies would be false positives, even though 95% of studies conducted would be correct negatives.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Which correction is more useful for keeping the alpha and FWER rates the same

viewof fwer2_response = Inputs.radio(['Bonferroni','Šidák']);
correct_fwer2 = 'Šidák';
fwer2_result = {
  if(fwer2_response == correct_fwer2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

False Discovery Rate

Question 1

Which of the following reflects false discovery rate:

viewof fdr_1_response = Inputs.radio(['False Positives/Negatives in the population','False Positves/Positives in the population','False positives/(False Positives + True Positives)']);
correct_fdr_1 = 'False positives/(False Positives + True Positives)';
fdr_1_result = {
  if(fdr_1_response == correct_fdr_1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

After ranking all the p-values which of the following is true about the Benjamini-Hochberg procedure:

viewof fdr_2_response = Inputs.radio(['You only accept p-values from the smallest to the largest until the first one that is above the corrected alpha value',"You accept all p-values that are smaller than the highest p-value below it's respective alpha threshold."]);
correct_fdr_2 = "You accept all p-values that are smaller than the highest p-value below it's respective alpha threshold.";
fdr_2_result = {
  if(fdr_2_response == correct_fdr_2){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Family-wise Error Rate vs. False Discovery Rate

Question 1

What association is there between the proportion of positive effects and FWER?

viewof fwer_vs_fdr1_response = Inputs.radio(['Positive','Neutral','Negative']);
correct_fwer_vs_fdr1 = 'Neutral';
fwer_vs_fdr1_result = {
  if(fwer_vs_fdr1_response == correct_fwer_vs_fdr1){
    return 'Correct!';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

What association is there between the proportion of positive effects and FDR?

viewof fwer_vs_fdr2_response = Inputs.radio(['Positive','Neutral','Negative']);
correct_fwer_vs_fdr2 = 'Negative';
fwer_vs_fdr2_result = {
  if(fwer_vs_fdr2_response == correct_fwer_vs_fdr2){
    return 'Correct! There should be a lower rate of false positives compared to false positives and true positives in a study that is investigating mostly positive effects compared to a study that is investigating mostly negative effects.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Permutations

Question 1

Permutation analysis can only be used on non-parametric data

viewof permutatations_1_response = Inputs.radio(['True','False']);
correct_permutatations_1 = 'False';
permutatations_1_result = {
  if(permutatations_1_response == correct_permutatations_1){
    return 'Correct! Whilst it is useful for analysis of non-parametric data, it is not restricted to use in these contexts. It would be valid to double check the conclusion of your parametric analysis, or for alternative analyses such compare how significant the difference is between two correlations.';
  } else {
    return 'Incorrect or incomplete.';
  };
}

Question 2

Permutation analysis can only be done when comparing 2 groups?

viewof permutatations_2_response = Inputs.radio(['True','False']);
correct_permutatations_2 = 'False';
permutatations_2_result = {
  if(permutatations_2_response == correct_permutatations_2){
    return 'Correct! It can be used on any analysis that generates a single output value (even if that single output value is a combination of other values). F-values from ANOVAs are an example of how you can compare between more than 2 groups. You can also compare between conditions within participants, but you would need to be mindful that you only permute swaps within participants for within-subject factors.';
  } else {
    return 'Incorrect or incomplete.';
  };
}