Statistics in Psychology

Descriptive Statistics

Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data (i.e. the sample) in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made. They are simply a way to describe our data.

The Distribution	The Central Tendency
The distribution is a summary of the frequency of individual values for a variable. One of the most common ways to describe a single variable is with a frequency distribution. A distribution may be displayed using percentages or depicted in graphical or tabular format, including histograms and stem-and-leaf display. The shape of the distribution may also be described via indices such as skewness and kurtosis.	The central tendency of a distribution is an estimate of the "center" of a distribution of values. There are three major types: Mean: all values in a set of data are added together and divided by the number of values (N). Median: this is the middle value when the data set is arranged in order from the lowest to the highest. Mode: this is the score that occurs the most often, i.e. the most popular score in a data set.
The Dispersion
Dispersion refers to the spread of the values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. The advantage of the range is that it is easy to calculate. The disadvantages are that it is distorted by extreme scores.	The standard deviation is the measure which tells us how scores are spread around the mean of the sample. In-other-words how much the scores “deviate” from the mean. The smaller the standard deviation, the closer together the values in the set are. A larger standard deviation shows that the values are more spread out from the mean.

Inferential Statistics

Inferential statistics allow the researcher to generalize their findings from the sample data to the larger population. They help assess the strength of the relationship between the independent (causal) variables, and the dependent (effect) variables. With inferential statistics, we are trying to reach conclusions that extend beyond the immediate data alone (i.e. our sample). For instance, we use inferential statistics to try to infer from the sample data what the population might think.

T-test	One-way ANOVA
A t-test is used when we have 1 IV with 2 levels. It estimates whether the population means under the 2 levels of the IV are different. The estimate is based on the difference between the measured sample means. There are two types of t-test. Independent t-test: between participants/ independent groups. Paired t-test: within participants/ repeated measures.	A one-way ANOVA is used when we have 1 IV with more than 2 levels. It estimates whether the population means under the different levels of the IV are different. An independent one-way ANOVA is used when there are different participants for each level of the IV (i.e. between participants). If the same participants are used for each level of the IV a one-way repeated measures (i.e. within subjects) ANOVA should be used.
Factorial ANOVAs	Correlation
Factorial ANOVAs are used to test for differences when we have more than one independet variable (IV). Including more than one IV, we can explore the effects of interactions between IVs. The terms ‘IV’ and ‘factor’ are interchangeable. ANOVAs with more than one IV are called Factorial ANOVAs. There are three broad Factorial ANOVA designs: all IVs are between-participants - Participants take part in only one condition (i.e. independent measures). all IVs are within-participants - Participants take part in all conditions (repeated measures). a mixture of between-participant and within-participant IVs - Participants take part in more than one, but not all conditions .	Correlation means association - more precisely it is a measure of the extent to which two variables are related. When working with continuous variables, the correlation coefficient to use is Pearson’s r. This is a numerical score showing the strength of a correlation. r = - 1 (perfect negative relationship) r = +1 (perfect positive relationship) r = 0 (no relationship) Once we’ve determined the relationship (Pearson's r) in our sample, inferential analyses allow us to determine the probability of measuring a relationship of that magnitude if the null hypothesis is true? Bivariate linear correlation involves measuring the linear relationship between two sample variables. Partial correlation allows us to examine the relationship between two variables, while removing the influence of a third variable.
Regression	Spearman's rho
While correlation assesses the relationship between x and y, regression allows us to predict y from x. For example, how much does y change as a result of a change in x? Linear regression allows us to assess if the score on x influenced the score on y. Multiple regression allows us to assess the effect that several predictor variables (e.g. x1, x2, x3 etc.) have on the outcome variable (y).	Spearman's rho is a non-parametric correlational analyses (an alternative to Pearson’s r). This test is used to determine if there is a correlation between sets of ranked data (ordinal data) or interval and ratio data that have been changed to ranks (ordinal data).
Mann-Whitney U	Wilcoxon T
Mann-Whitney U is a non-parametric alternative to an independent t-test. 1 IV, 2 levels: Between-participant design. The test evaluates whether there is a significant difference in the ranks assigned to the two IV levels.	Wilcoxon T is a non-parametric alternative to a paired t-test. Differences between scores in the two IV levels are calculated for each participant and then ranked . The test evaluates whether there is a significant difference in the ranks assigned to the two IV levels.
Chi-square	Friedman’s ANOVA
Also known as Goodness-of-Fit test. Deals with a single categorical variable - i.e. nominal level data. One-Variable Chi-square calculates the difference between expected and obtained frequencies. 2x2 Chi-Square (Test for Independence) measures the association between two categorical variables.	Friedman’s ANOVA is a non-parametric alternative to a repeated measures one-way ANOVA. . Tells you whether there is a significant difference, but not which IV levels are different. Conduct post-hoc tests (Wilcoxon T), corrected for multiple comparisons.