
Define Frequency Distribution and Cumulative Percentage
A frequency distribution is a table of rankordered scores that show the number of times that value occurred, or its frequency. Sometimes it is more meaningful to express frequencies as percentages of the total distribution.
A cumulative percentage is obtained by adding the percentage value for each score to all percentages that fall below that score.

What can a frequency distribution be displayed as?
A frequency distribution can be displayed as a histogram. A histogram is a bar graph composed of a series of columns, each representing one score or class interval. (p.370). It is used to show frequencies of data. Data in specified ranges are indicated by bars.
A frequency distribution can also be displayed as a cumulative frequency or cumulative distribution.

Define Normal Distribution, Skewed Distribution, and Normal Curve
A normal distribution is one in which the scores are evenly distributed above and below the mean, and each half is a mirror image of the other.
A skewed distribution is one in which the distribution of scores is asymmetrical about the mean. The degree to which the distribution deviates from symmetry is its skewness. Distributions can be positively skewed (skewed to the right, seen when most of the scores cluster at the low end of the causing the tail of the curve to point toward the right) or negatively skewed (skewed to the left)
Normal curve refers to a bellshaped distribution where most of the scores fall in the middle of the scale and progressively fewer fall at the extremes.

What are the 3 measures of central tendency
 Measures of Central Tendency
 Mean averaged value
 Median middle value
 Mode most common value

Define Percentiles and Quartiles
Percentiles describe a score’s position within a distribution by dividing the data into 100 equal portions. The location of a score on one of these portions represents its position relative to all other scores;
Quartiles divide a distribution into four equal parts, or quarters. Three quartiles exist for any data set Q1, Q2 , and Q3 corresponding to the 25th, 50th, and 75th percentile respectively. The median is the score at the 50th percentile. Distance between the first and the third quartiles is called the interquartile range.

Define Variance, deviation score, and standard deviation, and standard error of measurement
Variance (s2) is a measure of variability around the mean. (p. 376)
Deviation score = value – mean, = X – X(mean)
 Samples with larger deviation scores will be more variable about the mean.
 The sum of the squared deviation scores is called the sum of squares (SS).
 The variance is calculated by dividing the sum of squares by n1
Standard Deviation is the square root of the variance
Standard Error of Measurement = Standard deviation/n

Define Correlation, correlation coefficient, and coefficient of determination
Correlation reflects the degree of association between two sets of data, or the consistency of position within the two distributions
 Correlation coefficient – is a number between 1 and +1 whose sign is the same as the slope of the line and whose magnitude is related to the degree of linear association between two variables. Correlation coefficients closer to 1 indicate a stronger association between the two variables. The important quality of correlation coefficients is not their sign, but their absolute
 value. A correlation of 0.58 is stronger than a correlation of 0.43, even though with the former, the relationship is negative.
Coefficient of determination (r2). The square of the correlation coefficient, r2, indicates the percentage of the total variance in the Y score that can be explained by the X score.

Describe a norm referenced test and a criterion referenced test
 Normreferenced test
 A standardized testing instrument by which the testtaker's performance is interpreted in relation to the performance of a group of peers who have previously taken the same test. Although referred to as "normreferenced tests," they are really normreferenced interpretations of a score of a given test. Most standardized tests are normreferenced.
 Criterionreferenced test
 Tests developed to assess performance based on an absolute criterion. Scores are derived by comparing the performance of the testtaker to a prespecified standard or "criterion". Results are interpreted relative to a standard that represent an acceptable model or level of performance.

What is descriptive statistics?
 Have a very important role in describing distributions;
 Provide criteria to use specific statistical tests i.e. parametric vs nonparametric;
 Do not infer statistical inference but lays the foundation for the ability to perform statistics.

What is inferential statistics? Based on 2 things?

Inferential statistics provide estimates of population characteristics from a sample of data
 They are based on
 1) Probability (p. 387)
 o Likelihood that an event will happen.
 o Predicts what should happen not what will happen.
 2) Sampling error: the tendency of the data from the sample to differ from the population
 o The means from a number of samples is call a sampling distribution of means.
 o Standard error of the mean is the standard deviation of the means.

Define confidence intervals

Confidence Intervals (CI) (p. 392)
 A range of scores with specific boundaries that should contain the population mean
 The boundaries of the CI are based on the sample mean and its standard error
 Indicates level of confidence that mean of the population is within an interval

Define null hypothesis and alternative hypothesis
Null hypothesis (H0): It states that there is no difference (due to the intervention) and postulates that there will be no statistically significant difference between the groups.
 Alternative hypothesis (H1): This statement postulates that there will be a statistically significant difference between the two groups due to the intervention or the characteristics of the groups.
 Nondirectional hypothesis does not stipulate in advance the direction of the differences between the dependable variables of the groups.
 Directional hypothesis makes a specific prediction about the direction and nature of the differences between the dependent variables of the groups.

Define Type 1 and Type 2 error
 Type I error
 reject null when it is true.
 Eg. Conclude that treatment does make a difference when in fact it does not.
 Type II error
 do not reject null when it is false.
 Eg. Conclude that treatment does not make a difference when in fact it does.

Define a or level of significance

Also denoted as or alpha.
 Indicates the criterion for determining if the difference is statistically meaningful or ‘real’ rather than occurring due to chance.
 Researchers usually select a conservative or pvalue of <0.05
 This is often the maximal acceptable risk that the null hypothesis is not true.
 Determines probability of making type I error i.e reject null when it is true.


Indicates probability of not committing a type II error i.e. do not reject null when it is false.
 Probability of making type II error is denoted as or beta.
 Power is complement of 1 –
 If statistical power = 80%, then probability of not committing a type II error i.e. finding a treatment effect is 80%
 Increases when:
 o effect size increases;
 o variance of outcome decreases;
 o sample size increases;
 o or significance level is larger.

What is power analysis?
Power analysis is a procedure for estimating (a) the likelihood of committing a type II error, or (b) sample size requirements for a specific research design.
Need to perform power analysis when designing experiments to determine feasibility.

Directional Vs. Non Directional Tests

A directional test can be done when the direction of the treatment mean compared to the control mean can be anticipated.
Provides a more powerful comparison i.e. more likely to find a significant difference.

Parametric (3 types) vs. non parametric tests (2 types)
 Parametric tests can be used when the following criteria are fulfilled:
 o Variables of each group are normally distributed (the normality assumption).
 o The normal distributions have the same standard deviation (the assumption of homogeneity of variance)
 o The data is from an interval or ratio scale
 o Random samples
 o Examples of parametric tests
  ttest
  analysis of variance (ANOVA)
  posthoc tests
 Nonparametric are used in the following situations:
 o Variables are comprised of ordinal data
 o Small samples that have not satisfied normality or equality of variance.
 o Nominal or ordinal data
 o Examples of nonparametric tests
  Mann Whitney U Test
  Friedman twoway ANOVA by ranks

What is a TTest
Parametric Test
 Simplest experimental design
 2 randomly selected groups
 1 receives control; other receives treatment
A ttest examines means and variances of each group to determine if the two groups are statistically different. Paired ttests can be used for matched subjects or prepost test designs

What is an ANOVA (both types)
Parametric Test
 Compares 3 or more conditions, groups, or treatments
 Can be independent groups or repeated measures
 Calculates an Fstatistic which indicates a significant difference between at least 2 means but does not indicate which groups are different
 1)Multiple groups design
 Tested at one time point
 Eg. How does muscle soreness after eccentric exercise differ in those who are under 20 years of age, those 2140 years of age and those 4160 years of age?
 2)2way ANOVA
 Tested at several time points
 Eg. How does muscle soreness after eccentric exercise differ in those who are under 20 years of age, those 2140 years of age and those 4160 years of age at different time points – baseline, 1, 2, or 3 days after the exercise stimulus?

What is a multiple comparisons test? (3 types)
Parametric Test
 Posthoc Tests
 These tests are classified as post hoc because specific comparisons are decided after performing the ANOVA
 Some are a priori or planned comparisons before the ANOVA was performed.
 o Tukey’s honestly significant difference (very conservative. Type I error low)
 o Newman Keul’s is not as conservative
 o Bonferroni’s correction

What is the MannWhitney U Test (Wilcoxon)
Nonparametric Test
 Nonparametric counterpart of two sample (unpaired) ttest
 Used when the variables do not meet the parametric criteria
 Does not require equal n of both groups
 Wilcoxon’s test is used for paired data sets

What is the Friedman Twoway ANOVA by ranks?
Non Parametric Test
 ANOVA by ranks
 Also called Friedman Chisquare test
 Nonparametric equivalent of the twoway ANOVA

