Welcome to Part 3 of 4 of the Using Data to Make Data-Driven Instructional Decisions Blog Series! Today, in Part 3, we are going to focus on using statistics to transform our data into knowledge. Statistical analysis on a data set allows educators to essentially mine information from the data. What this does is provide us with newfound information we did not have before that is derived from the data. This new information and knowledge can then be used to make strategic decisions. In online, in-person, and blended classroom and school settings, it is our job as educators to make decisions grounded in evidence. Ultimately, the data set were able to statistically analyze becomes the needed evidence to support our decision. Furthermore, the purpose of this post of this blog series is to provide K-12 educators with a blueprint of how to conduct basic univariate and multivariate statistical analysis by teaching them how to use statistical formula’s on the data they collect in their classrooms and schools so they can transform that data into knowledge to make critical and strategic instructional decisions.

** Univariate (Descriptive) Statistics**

Univariate statistical, also known as descriptive statistics, involves a single variable of analysis. For example, say we were working with a classes recent overall scores of a math test. Through univariate statistics, we are able to summarize those scores and see how those scores breakdown to illustrate how all of the students did on the math test. This is how the word “descriptive” comes into play because the statistical outputs describe what is happening throughout the data set of math test scores.

Univariate statistics describes the frequency of values, which refers to how many times a data point from a data set can be grouped or categorized together. When we think of the average (i.e., mean), this is describing the central tendency of the values of the data set. The mean, median, and mode are all univariate statistical calculations that relate to the distribution of data found within a data set. All of these univariate formulas can help a teacher or school leader see beyond just the initial math scores of the students to group and categorize various groups of students based on their performance.

What can we do with this new information derived from these univariate statistical formulas? We can see how many students fell close to the overall mean score of the math test as well as group students who exceeded the mean score and those who did not exceed the mean score. Beyond just looking at the overall test score, we can look at the questions on the exam and conduct the same statistical calculations. This can allow teachers to see which students need more support in mastering a concept in addition to students who will need more enrichment since they already mastered the concept assessed. In addition, we want to note that you can do this for formative and summative assessments, which allows us to make strategic decisions quickly and efficiently, if needed.

Ultimately, this is just the tip of the iceberg of what you can do with univariate statistics and the student data we collect. What’s great about univariate statistics is that the data visualizations in the form of graphs you can create can help with interpreting the data trends found within a data set. Once the initial univariate data analysis is conducted, it’s always a good idea to create data visualizations to further analyze trends. These same visualizations can be used at a later time, if needed, to articulate the newfound knowledge and trends to stakeholders.

**Multivariate Statistics**

Beyond univariate statistics, we also want to conduct statistical analysis on data to see whether relationships exist multiple variables. For example, one variable could be the final math assessment scores from your class and the other variable could be the number of days students were absent throughout the semester. We can use statistics to determine whether a relationship exists between two or more variables. There are many types of multivariate statistical formulas that can be computed to determine whether relationships exist between multiple variables. Generally, correlations, t-tests, ANOVA’s, and regressions are common basic multivariate statistical calculations that can be performed on a data set.

One example of how conducting a multivariate statistical formula like a correlation can help K-12 educators is in determining a whether a relationship exists between the reading levels of a class or grade level and their performance on the end of the year state assessment. With a correlation, we can see if there is a significant positive or negative relationship exists relationship between the student reading levels and assessment. Furthermore, we can conduct this same calculation across all groups of students, grade levels, and schools. Thus, we can see whether statistical relationships exists among different sets of data to help inform our instruction. What this does is provide us with a guide to further investigate what’s happening with students taking the assessment as well as what reading skills may be required for students to learn to do well on the assessment. This is powerful as it can help us focus our curriculum and instruction on essential skills to help students do better on the assessment in the future.

**Note: **For the purposes of this post, p-value, variables, and types of data are not discussed. These are all essential to multivariate statistics, but require much more of an explanation. My goal is to show how to conduct these calculations instead of providing the full Statistics 101 explanation.

**Common** **Univariate and Multivariate Statistical Formulas – Excel and Sheets**

Statistical formulas on Excel and Sheets allow us to perform a statistical analysis on a data set. Before getting into the formula’s, there are several steps that are required in order for them to be computed properly without producing an error. Before getting into the three steps of inputting formula’s and the data into them, there are a number of univariate and multivariate statistical formula’s on both Microsoft Excel and Google Sheets that all educators should know about so they can conduct statistical analysis on their collected data.

Statistical Function Formula | What does it do? |

=COUNT(value1, [value2],…) | Counts the numeric values supplied in a data set. An example of this would be counting the number of times 10 comes up within a data set. |

=COUNTA(value1, [value2],…) or COUNTA(โeducationโ, A10:A20) | Counts all of the numeric values or text of non-blanks within a data set. |

=FREQUENCY(data_array, bins_array) Note: data_array is the original values for the frequency that is about to be calculated. Then, bins_arrary is the value that sets the limits of ranges to be split into. | Determines the frequency of value(s) within a data set. |

=AVERAGE(number 1, number 2) | Determines the mean within a data set. An example of how this can be represented using a data set is =AVERAGE(A1:A300). |

=MIN(number 1, number 2) | Determines the minimum value (i.e., smallest value) within a data set. |

=MAX(number 1, number 2) | Determines the highest value (i.e., largest value) within a data set. |

=MEDIAN(number 1, number 2) | Determines the median within a data set. |

=MODE(number 1, number 2) | Determines the mode within a data set. |

=SUM(number 1, number 2) | Determines the sum of multiple values within a data set. |

=STDEV.P(number 1, number 2) | Calculates the standard deviation of an entire population (i.e., A2:A300). |

=IF(logical_test[value_if_true], [value_if_false]) | If, then conditional statement. This allows for the identification of pieces of data based on a condition (i.e., =IF(B2<60, โFailโ,โPassโ)). |

=CORREL(column 1, column 2) | Calculates a Pearsonโs r that represents a possible correlational relationship between two different data sets (i.e.,=CORREL(a2:a100, b2:b100). |

=T.TEST(column 1) or =T.TEST(column 1, column 2) | Calculates the p-value of a single set or multiple data sets. |

**Conducting Statistical Analysis Steps on Excel and Sheets** **& Video Demonstrations**

As promised above, with the statistical formula’s that have been given, follow this three step process in conducting the univariate or multivariate statistical data analysis with the data collected in your classroom or school. After review steps one through three, take a look at each video posted on computing univariate and multivariate statistical analysis for an in-depth look at how it is done.

**Step 1: In a Data Cell, Type Out the Statistical Formula**

**Step 2: Select the Range of Data for the Calculation and Place into Formula**

**Step 3: Click “Enter” to Calculate the Inputted Data into the Formula**

Once these steps are performed on the selected data, there will be a solution output within the cell you typed in your statistical formula. This solution from the statistical formula is the newfound knowledge that has been calculated from your data. Now think about these three steps as you watch the two videos below.

**Univariate Statistics: A Video Demonstration**

**Multivariate Statistics: Correlation & Regression** **Demonstration**

In the video demonstrating the correlation and regression, think about if you replaced height and weight with the variables of reading levels (i.e., Lexile, DRA, etc.), grade point average, or test scores. In the same manner, we can use the same methodology to compute correlations and regressions on Excel and Sheets.

**Conclusion**

Now that we have seen how to conduct some basic univariate and multivariate statistical analysis, we will cover next week in Part 4 of the blog series is on how this newfound knowledge from the statistical analysis can be put into decision-making frameworks and action plans to help teachers and school leaders make instructional decisions. My hope is that you have an idea of how to take some of the data you collect in your classroom and transform it into useful knowledge to help you as an instructor or leader help put your students in the best instructional position to succeed and learn.

Ultimately, what we covered in this post is the tip of the iceberg. What we discussed here are some of the basic. Some important details about p-values, variables, and the types of data were left out. However, the purpose for this post is to show how to conduct some basic calculations instead of taking a Statistics 101 course. What we have done here takes practice, but it’s completely doable. Also, it can be done quite quickly if you have clean data. I suggest taking a look back at Part 1 and 2 of this blog series to review once again after reading through today’s post.

If you have any questions or comments about today’s post, please make sure you leave one below or on Twitter!

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